Asymptotic expansions for elliptic-like regularizations of semilinear evolution equations
Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by th...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Ahsan, M. [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014transfer abstract |
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| Umfang: |
24 |
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| Übergeordnetes Werk: |
Enthalten in: Effects of temperature on adsorption and oxidative degradation of bisphenol A in an acid-treated iron-amended granular activated carbon - Kim, Jihyun R. ELSEVIER, 2015, Orlando, Fla |
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| Übergeordnetes Werk: |
volume:257 ; year:2014 ; number:8 ; day:15 ; month:10 ; pages:2926-2949 ; extent:24 |
| Links: |
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| DOI / URN: |
10.1016/j.jde.2014.06.004 |
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ELV039547299 |
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| 520 | |a Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . | ||
| 520 | |a Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . | ||
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10.1016/j.jde.2014.06.004 doi GBVA2014022000017.pica (DE-627)ELV039547299 (ELSEVIER)S0022-0396(14)00274-5 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 660 VZ 530 600 670 VZ 51.00 bkl Ahsan, M. verfasserin aut Asymptotic expansions for elliptic-like regularizations of semilinear evolution equations 2014transfer abstract 24 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . 34G20 Elsevier 34K26 Elsevier Moroşanu, G. oth Enthalten in Elsevier Kim, Jihyun R. ELSEVIER Effects of temperature on adsorption and oxidative degradation of bisphenol A in an acid-treated iron-amended granular activated carbon 2015 Orlando, Fla (DE-627)ELV012753777 volume:257 year:2014 number:8 day:15 month:10 pages:2926-2949 extent:24 https://doi.org/10.1016/j.jde.2014.06.004 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_24 GBV_ILN_40 GBV_ILN_105 51.00 Werkstoffkunde: Allgemeines VZ AR 257 2014 8 15 1015 2926-2949 24 045F 510 |
| spelling |
10.1016/j.jde.2014.06.004 doi GBVA2014022000017.pica (DE-627)ELV039547299 (ELSEVIER)S0022-0396(14)00274-5 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 660 VZ 530 600 670 VZ 51.00 bkl Ahsan, M. verfasserin aut Asymptotic expansions for elliptic-like regularizations of semilinear evolution equations 2014transfer abstract 24 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . 34G20 Elsevier 34K26 Elsevier Moroşanu, G. oth Enthalten in Elsevier Kim, Jihyun R. ELSEVIER Effects of temperature on adsorption and oxidative degradation of bisphenol A in an acid-treated iron-amended granular activated carbon 2015 Orlando, Fla (DE-627)ELV012753777 volume:257 year:2014 number:8 day:15 month:10 pages:2926-2949 extent:24 https://doi.org/10.1016/j.jde.2014.06.004 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_24 GBV_ILN_40 GBV_ILN_105 51.00 Werkstoffkunde: Allgemeines VZ AR 257 2014 8 15 1015 2926-2949 24 045F 510 |
| allfields_unstemmed |
10.1016/j.jde.2014.06.004 doi GBVA2014022000017.pica (DE-627)ELV039547299 (ELSEVIER)S0022-0396(14)00274-5 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 660 VZ 530 600 670 VZ 51.00 bkl Ahsan, M. verfasserin aut Asymptotic expansions for elliptic-like regularizations of semilinear evolution equations 2014transfer abstract 24 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . 34G20 Elsevier 34K26 Elsevier Moroşanu, G. oth Enthalten in Elsevier Kim, Jihyun R. ELSEVIER Effects of temperature on adsorption and oxidative degradation of bisphenol A in an acid-treated iron-amended granular activated carbon 2015 Orlando, Fla (DE-627)ELV012753777 volume:257 year:2014 number:8 day:15 month:10 pages:2926-2949 extent:24 https://doi.org/10.1016/j.jde.2014.06.004 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_24 GBV_ILN_40 GBV_ILN_105 51.00 Werkstoffkunde: Allgemeines VZ AR 257 2014 8 15 1015 2926-2949 24 045F 510 |
| allfieldsGer |
10.1016/j.jde.2014.06.004 doi GBVA2014022000017.pica (DE-627)ELV039547299 (ELSEVIER)S0022-0396(14)00274-5 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 660 VZ 530 600 670 VZ 51.00 bkl Ahsan, M. verfasserin aut Asymptotic expansions for elliptic-like regularizations of semilinear evolution equations 2014transfer abstract 24 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . 34G20 Elsevier 34K26 Elsevier Moroşanu, G. oth Enthalten in Elsevier Kim, Jihyun R. ELSEVIER Effects of temperature on adsorption and oxidative degradation of bisphenol A in an acid-treated iron-amended granular activated carbon 2015 Orlando, Fla (DE-627)ELV012753777 volume:257 year:2014 number:8 day:15 month:10 pages:2926-2949 extent:24 https://doi.org/10.1016/j.jde.2014.06.004 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_24 GBV_ILN_40 GBV_ILN_105 51.00 Werkstoffkunde: Allgemeines VZ AR 257 2014 8 15 1015 2926-2949 24 045F 510 |
| allfieldsSound |
10.1016/j.jde.2014.06.004 doi GBVA2014022000017.pica (DE-627)ELV039547299 (ELSEVIER)S0022-0396(14)00274-5 DE-627 ger DE-627 rakwb eng 510 510 DE-600 660 VZ 660 VZ 530 600 670 VZ 51.00 bkl Ahsan, M. verfasserin aut Asymptotic expansions for elliptic-like regularizations of semilinear evolution equations 2014transfer abstract 24 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . 34G20 Elsevier 34K26 Elsevier Moroşanu, G. oth Enthalten in Elsevier Kim, Jihyun R. ELSEVIER Effects of temperature on adsorption and oxidative degradation of bisphenol A in an acid-treated iron-amended granular activated carbon 2015 Orlando, Fla (DE-627)ELV012753777 volume:257 year:2014 number:8 day:15 month:10 pages:2926-2949 extent:24 https://doi.org/10.1016/j.jde.2014.06.004 Volltext GBV_USEFLAG_U GBV_ELV SYSFLAG_U GBV_ILN_22 GBV_ILN_24 GBV_ILN_40 GBV_ILN_105 51.00 Werkstoffkunde: Allgemeines VZ AR 257 2014 8 15 1015 2926-2949 24 045F 510 |
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Enthalten in Effects of temperature on adsorption and oxidative degradation of bisphenol A in an acid-treated iron-amended granular activated carbon Orlando, Fla volume:257 year:2014 number:8 day:15 month:10 pages:2926-2949 extent:24 |
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Effects of temperature on adsorption and oxidative degradation of bisphenol A in an acid-treated iron-amended granular activated carbon |
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asymptotic expansions for elliptic-like regularizations of semilinear evolution equations |
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Asymptotic expansions for elliptic-like regularizations of semilinear evolution equations |
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Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . |
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Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . |
| abstract_unstemmed |
Consider in a real Hilbert space H the Cauchy problem ( P 0 ): u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , where −A is the infinitesimal generator of a C 0 -semigroup of contractions, B is a nonlinear monotone operator, and f is a given H-valued function. Inspired by the excellent book on singular perturbations by J.L. Lions, we associate with problem ( P 0 ) the following regularization ( P ε ): − ε u ″ ( t ) + u ′ ( t ) + A u ( t ) + B u ( t ) = f ( t ) , 0 ≤ t ≤ T ; u ( 0 ) = u 0 , u ′ ( T ) = u T , where ε > 0 is a small parameter. We investigate existence, uniqueness and higher regularity for problem ( P ε ). Then we establish asymptotic expansions of order zero, and of order one, for the solution of ( P ε ). Problem ( P ε ) turns out to be regularly perturbed of order zero, and singularly perturbed of order one, with respect to the norm of C ( [ 0 , T ] ; H ) . However, the boundary layer of order one is not visible through the norm of L 2 ( 0 , T ; H ) . |
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Asymptotic expansions for elliptic-like regularizations of semilinear evolution equations |
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