Interface Development and Local Solutions to Reaction-Diffusion Equations

DOI10.1137/S003614109732986XzbMath0964.35086OpenAlexW1981724786MaRDI QIDQ4509951

John R. King, Ugur G. Abdulla

Publication date: 19 October 2000

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/s003614109732986x

zbMATH Keywords

Cauchy problemlocal solutionsnonlinear degenerate parabolic equationsevolution of interfacesexplicit formulae for the interfaceshort-time behavior of the interface

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Flows in porous media; filtration; seepage (76S05) Degenerate parabolic equations (35K65) Solutions to PDEs in closed form (35C05)

Related Items (13)

Evolution of interfaces and explicit asymptotics at infinity for the fast diffusion equation with absorption ⋮ Evolution of interfaces for the nonlinear parabolic p-Laplacian-type reaction-diffusion equations. II. Fast diffusion vs. absorption ⋮ Well-posedness of the Dirichlet problem for the non-linear diffusion equation in non-smooth domains ⋮ Evolution of interfaces for the non-linear parabolic p-Laplacian type reaction–diffusion equations ⋮ Interface development for the nonlinear degenerate multidimensional reaction-diffusion equations. II: Fast diffusion versus absorption ⋮ Interfaces in diffusion-absorption processes in nonhomogeneous media ⋮ Reaction-diffusion in nonsmooth and closed domains ⋮ Evolution of interfaces for the nonlinear double degenerate parabolic equation of turbulent filtration with absorption ⋮ On the Dirichlet problem for the nonlinear diffusion equation in non-smooth domains ⋮ Interface development for the nonlinear degenerate multidimensional reaction-diffusion equations ⋮ Existence and uniqueness of very singular solution of a degenerate parabolic equation with nonlinear convection ⋮ Reaction-diffusion in a closed domain formed by irregular curves ⋮ Reaction-diffusion in irregular domains

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