Spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advection-diffusion equations

Yuki Kaneko; Hiroshi Matsuzawa

doi:10.1016/j.jmaa.2015.02.051

Spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advection-diffusion equations

Yuki Kaneko, Hiroshi Matsuzawa^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

45 Citations (Scopus)

Abstract

In this study, we consider free boundary problems for nonlinear advection-diffusion equations of the form u_t-u_xx+β_{u_x}=f(u) for t>0, g(t)2-norm as t→∞ when spreading occurs. We develop new approaches and extend a previous result to the problem with the advection term.

Original language	English
Pages (from-to)	43-76
Number of pages	34
Journal	Journal of Mathematical Analysis and Applications
Volume	428
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2015.02.051
Publication status	Published - 2015

Keywords

Bistable
Combustion
Free boundary problem
Monostable
Nonlinear advection-diffusion equation
Spreading speed

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2015.02.051

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title = "Spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advection-diffusion equations",

abstract = "In this study, we consider free boundary problems for nonlinear advection-diffusion equations of the form ut-uxx+βux=f(u) for t>0, g(t)2-norm as t→∞ when spreading occurs. We develop new approaches and extend a previous result to the problem with the advection term.",

keywords = "Bistable, Combustion, Free boundary problem, Monostable, Nonlinear advection-diffusion equation, Spreading speed",

author = "Yuki Kaneko and Hiroshi Matsuzawa",

year = "2015",

doi = "10.1016/j.jmaa.2015.02.051",

language = "English",

volume = "428",

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journal = "Journal of Mathematical Analysis and Applications",

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AU - Kaneko, Yuki

AU - Matsuzawa, Hiroshi

PY - 2015

Y1 - 2015

N2 - In this study, we consider free boundary problems for nonlinear advection-diffusion equations of the form ut-uxx+βux=f(u) for t>0, g(t)2-norm as t→∞ when spreading occurs. We develop new approaches and extend a previous result to the problem with the advection term.

AB - In this study, we consider free boundary problems for nonlinear advection-diffusion equations of the form ut-uxx+βux=f(u) for t>0, g(t)2-norm as t→∞ when spreading occurs. We develop new approaches and extend a previous result to the problem with the advection term.

KW - Bistable

KW - Combustion

KW - Free boundary problem

KW - Monostable

KW - Nonlinear advection-diffusion equation

KW - Spreading speed

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AN - SCOPUS:84934443398

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

Spreading speed and sharp asymptotic profiles of solutions in free boundary problems for nonlinear advection-diffusion equations

Abstract

Keywords

ASJC Scopus subject areas

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