Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation

Abstract This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then w...
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Autor*in:	Sheng, WeiJie [verfasserIn] Li, WanTong [verfasserIn] Wang, ZhiCheng [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	Allen-Cahn equation asymptotic stability multidimensional V-shaped traveling front

Übergeordnetes Werk:	Enthalten in: Science in China - Asheville, NC : Science in China Press, 1995, 56(2013), 10 vom: 09. Aug., Seite 1969-1982
Übergeordnetes Werk:	volume:56 ; year:2013 ; number:10 ; day:09 ; month:08 ; pages:1969-1982

Links:	Volltext

DOI / URN:	10.1007/s11425-013-4699-5

Katalog-ID:	SPR01913617X

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520			\|a Abstract This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle.
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allfields	10.1007/s11425-013-4699-5 doi (DE-627)SPR01913617X (SPR)s11425-013-4699-5-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Sheng, WeiJie verfasserin aut Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle. Allen-Cahn equation (dpeaa)DE-He213 asymptotic stability (dpeaa)DE-He213 multidimensional (dpeaa)DE-He213 V-shaped (dpeaa)DE-He213 traveling front (dpeaa)DE-He213 Li, WanTong verfasserin aut Wang, ZhiCheng verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 56(2013), 10 vom: 09. Aug., Seite 1969-1982 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:56 year:2013 number:10 day:09 month:08 pages:1969-1982 https://dx.doi.org/10.1007/s11425-013-4699-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 56 2013 10 09 08 1969-1982
spelling	10.1007/s11425-013-4699-5 doi (DE-627)SPR01913617X (SPR)s11425-013-4699-5-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Sheng, WeiJie verfasserin aut Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle. Allen-Cahn equation (dpeaa)DE-He213 asymptotic stability (dpeaa)DE-He213 multidimensional (dpeaa)DE-He213 V-shaped (dpeaa)DE-He213 traveling front (dpeaa)DE-He213 Li, WanTong verfasserin aut Wang, ZhiCheng verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 56(2013), 10 vom: 09. Aug., Seite 1969-1982 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:56 year:2013 number:10 day:09 month:08 pages:1969-1982 https://dx.doi.org/10.1007/s11425-013-4699-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 56 2013 10 09 08 1969-1982
allfields_unstemmed	10.1007/s11425-013-4699-5 doi (DE-627)SPR01913617X (SPR)s11425-013-4699-5-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Sheng, WeiJie verfasserin aut Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle. Allen-Cahn equation (dpeaa)DE-He213 asymptotic stability (dpeaa)DE-He213 multidimensional (dpeaa)DE-He213 V-shaped (dpeaa)DE-He213 traveling front (dpeaa)DE-He213 Li, WanTong verfasserin aut Wang, ZhiCheng verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 56(2013), 10 vom: 09. Aug., Seite 1969-1982 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:56 year:2013 number:10 day:09 month:08 pages:1969-1982 https://dx.doi.org/10.1007/s11425-013-4699-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 56 2013 10 09 08 1969-1982
allfieldsGer	10.1007/s11425-013-4699-5 doi (DE-627)SPR01913617X (SPR)s11425-013-4699-5-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Sheng, WeiJie verfasserin aut Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle. Allen-Cahn equation (dpeaa)DE-He213 asymptotic stability (dpeaa)DE-He213 multidimensional (dpeaa)DE-He213 V-shaped (dpeaa)DE-He213 traveling front (dpeaa)DE-He213 Li, WanTong verfasserin aut Wang, ZhiCheng verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 56(2013), 10 vom: 09. Aug., Seite 1969-1982 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:56 year:2013 number:10 day:09 month:08 pages:1969-1982 https://dx.doi.org/10.1007/s11425-013-4699-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 56 2013 10 09 08 1969-1982
allfieldsSound	10.1007/s11425-013-4699-5 doi (DE-627)SPR01913617X (SPR)s11425-013-4699-5-e DE-627 ger DE-627 rakwb eng 510 530 520 ASE 30.00 bkl 31.00 bkl Sheng, WeiJie verfasserin aut Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle. Allen-Cahn equation (dpeaa)DE-He213 asymptotic stability (dpeaa)DE-He213 multidimensional (dpeaa)DE-He213 V-shaped (dpeaa)DE-He213 traveling front (dpeaa)DE-He213 Li, WanTong verfasserin aut Wang, ZhiCheng verfasserin aut Enthalten in Science in China Asheville, NC : Science in China Press, 1995 56(2013), 10 vom: 09. Aug., Seite 1969-1982 (DE-627)325695059 (DE-600)2038800-7 1862-2763 nnns volume:56 year:2013 number:10 day:09 month:08 pages:1969-1982 https://dx.doi.org/10.1007/s11425-013-4699-5 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OPC-MAT SSG-OPC-AST SSG-OPC-ASE GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_152 GBV_ILN_161 GBV_ILN_171 GBV_ILN_187 GBV_ILN_224 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 30.00 ASE 31.00 ASE AR 56 2013 10 09 08 1969-1982
language	English
source	Enthalten in Science in China 56(2013), 10 vom: 09. Aug., Seite 1969-1982 volume:56 year:2013 number:10 day:09 month:08 pages:1969-1982
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author	Sheng, WeiJie
spellingShingle	Sheng, WeiJie ddc 510 bkl 30.00 bkl 31.00 misc Allen-Cahn equation misc asymptotic stability misc multidimensional misc V-shaped misc traveling front Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation
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topic_title	510 530 520 ASE 30.00 bkl 31.00 bkl Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation Allen-Cahn equation (dpeaa)DE-He213 asymptotic stability (dpeaa)DE-He213 multidimensional (dpeaa)DE-He213 V-shaped (dpeaa)DE-He213 traveling front (dpeaa)DE-He213
topic	ddc 510 bkl 30.00 bkl 31.00 misc Allen-Cahn equation misc asymptotic stability misc multidimensional misc V-shaped misc traveling front
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title	Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation
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title_full	Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation
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title_sort	multidimensional stability of v-shaped traveling fronts in the allen-cahn equation
title_auth	Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation
abstract	Abstract This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle.
abstractGer	Abstract This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle.
abstract_unstemmed	Abstract This paper is concerned with the multidimensional asymptotic stability of V-shaped traveling fronts in the Allen-Cahn equation under spatial decaying initial values. We first show that V-shaped traveling fronts are asymptotically stable under the perturbations that decay at infinity. Then we further show that there exists a solution that oscillates permanently between two V-shaped traveling fronts, which indicates that V-shaped traveling fronts are not always asymptotically stable under general bounded perturbations. Our main technique is the supersolutions and subsolutions method coupled with the comparison principle.
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title_short	Multidimensional stability of V-shaped traveling fronts in the Allen-Cahn equation
url	https://dx.doi.org/10.1007/s11425-013-4699-5
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up_date	2024-07-04T00:19:48.749Z
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