Traveling Wave Solution for Some Nonlinear Diffusion Equations
- 1 November 1981
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 12 (6) , 880-892
- https://doi.org/10.1137/0512074
Abstract
Traveling wave solutions are discussed for nonlinear diffusion equations where the nonlinearity occurs in the diffusion flux as well as in a source term. For a variety of nonlinear diffusion fluxes it is shown that wave solutions exist if and only if the wave speed is greater than some critical value. This critical value is determined explicitly in some special cases, and inequalities are derived for the general case.Keywords
This publication has 10 references indexed in Scilit:
- Density-Dependent Interaction–Diffusion SystemsPublished by Elsevier ,1980
- Some qualitative properties of solutions of a generalised diffusion equationMathematical Proceedings of the Cambridge Philosophical Society, 1979
- Asymptotic states for equations of reaction and diffusionBulletin of the American Mathematical Society, 1978
- The approach of solutions of nonlinear diffusion equations to travelling front solutionsArchive for Rational Mechanics and Analysis, 1977
- On the diffusion of biological populationsMathematical Biosciences, 1977
- The regulation of inhomogeneous populationsJournal of Theoretical Biology, 1975
- Nonlinear diffusion in population genetics, combustion, and nerve pulse propagationPublished by Springer Nature ,1975
- Regularity Propeties of Flows Through Porous MediaSIAM Journal on Applied Mathematics, 1969
- On a first-order boundary value problem from laminar flame theoryArchive for Rational Mechanics and Analysis, 1963
- Laminar flame theory and the steady, linear burning of a monopropellantArchive for Rational Mechanics and Analysis, 1963