Front-like entire solutions for equations with convection

E. C.M. Crooks, Je Chiang Tsai

研究成果: 雜誌貢獻期刊論文同行評審

15 引文 斯高帕斯(Scopus)

摘要

We construct families of front-like entire solutions for problems with convection, both for bistable and monostable reaction-diffusion-convection equations, and, via vanishing-viscosity arguments, for bistable and monostable balance laws. The unified approach employed is inspired by ideas of Chen and Guo and based on a robust method using front-dependent sub and supersolutions. Unlike convectionless problems, the equations studied here lack symmetry between increasing and decreasing travelling waves, which affects the choice of sub and supersolutions used. Our entire solutions include both those that behave like two fronts coming together and annihilating as time increases, and, for bistable equations, those that behave like two fronts merging to propagate like a single front. We also characterise the long-time behaviour of each family of entire solutions, which in the case of solutions constructed from a monostable front merging with a bistable front answers a question that was open even for reaction-diffusion equations without convection.

原文英語
頁(從 - 到)1206-1249
頁數44
期刊Journal of Differential Equations
253
發行號4
DOIs
出版狀態已發佈 - 2012 八月 15

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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