A very singular solution and other self-similar solutions of the heat equation with convection

DOI10.1016/0362-546X(95)90094-ZzbMath0824.35058MaRDI QIDQ4328010

H. C. Serafini, Lambertus A. Peletier

Publication date: 24 October 1995

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

self-similar solutionvery singular solutionheat equation with convection

Mathematics Subject Classification ID

Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations (35K60)

Related Items (7)

Complete classification of shape functions of self-similar solutions ⋮ Singular solutions and asymptotic behaviour for a class of conservation laws with absorption ⋮ A very singular solution for the slow diffusion equation with nonlinear convection ⋮ Unnamed Item ⋮ Existence and uniqueness of very singular solution of a degenerate parabolic equation with nonlinear convection ⋮ Existence and uniqueness of a non-negative monotonic solution of a nonlinear ordinary differential equation ⋮ Analysis of the self-similar solutions of the nonplanar Burgers equation

Cites Work

• Unnamed Item
• Large time behavior of the solutions of a semilinear parabolic equation in \(\mathbb R^ n\)
• Thermal waves in an absorbing and convecting medium
• A very singular solution of the heat equation with absorption
• Existence and uniqueness on the very singular solution of the porous media equation with absorption
• Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption
• A necessary and sufficient condition for the existence of an interface in flows through porous media
• A very singular solution of the porous media equation with absorption
• A Very Singular Solution of a Quasilinear Degenerate Diffusion Equation With Absorption
• Self-Similar Solutions of a Convection Diffusion Equation And Related Semilinear Elliptic Problems
• ASYMPTOTIC PROFILES WITH FINITE MASS IN ONE-DIMENSIONAL CONTAMINANT TRANSPORT THROUGH POROUS MEDIA: THE FAST REACTION CASE
• Long-Time Behavior for a Convection-Diffusion Equation in Higher Dimensions

This page was built for publication: A very singular solution and other self-similar solutions of the heat equation with convection