Emergence of Waves in a Nonlinear Convection-Reaction-Diffusion Equation-Reference-Cited by-同舟云学术

Emergence of Waves in a Nonlinear Convection-Reaction-Diffusion Equation

Published:2004-08-01 Issue:3 Volume:4 Page:251-272
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Kamin Shoshana¹,Rosenau Philip¹

Affiliation:

1. School of Mathematical Sciences, Tel Aviv University Tel Aviv 69978, Israel

Abstract

Abstract In this work we prove that for some class of initial data the solution of the Cauchy problem ut = (um)xx + a(um)x + u(1 - um-1), x ∈ ℝ; t > 0 u(0; x) = u0(x), u0(x) ≥ 0 approaches the travelling solution, spreading either to the right or to the left, or two travelling waves moving in opposite directions.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2004-0302/pdf

Reference7 articles.

1. The behaviour of solutions of the Cauchy problem when the time tends to infinity in the case of quasilinear equations arising in the theory of combustion Soviet Math Translation of : Dokl;Kanel;Dokl Akad Nauk SSSR,1960

2. Some problems of the qualitative theory of non - linear degenerate second - order parabolic equations Russian Math;Kalashnikov;Surv,1987

3. The behaviour of solutions of some nonlinear diffusion equations for large time Kyoto Univ An introduction to the mathematical theory of the porous medium equa - tion Shape Optimization and Free Boundaries Kluwer Acad Dodrecht;Uchiyama;Math Publ,1978

4. Some exact solutions to a nonlinear diffusion problem in population genetics and combustion;Newman;Theor Biol,1980

5. Reaction and concentration dependent diffusion model;Rosenau;Rev Let,2002

Cited by 14 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Convergence to Sharp Traveling Waves of Solutions for Burgers-Fisher-KPP Equations with Degenerate Diffusion;Journal of Nonlinear Science;2024-03-16

2. Looking forwards and backwards: Dynamics and genealogies of locally regulated populations;Electronic Journal of Probability;2024-01-01

3. Construction of multiple new analytical soliton solutions and various dynamical behaviors to the nonlinear convection-diffusion-reaction equation with power-law nonlinearity and density-dependent diffusion via Lie symmetry approach together with a couple of integration approaches;Journal of Ocean Engineering and Science;2022-01

4. Propagation of solutions of the Porous Medium Equation with reaction and their travelling wave behaviour;Nonlinear Analysis;2020-06

5. Logarithmic corrections in Fisher–KPP type porous medium equations;Journal de Mathématiques Pures et Appliquées;2020-04