Self-Similar Solutions of a Convection Diffusion Equation And Related Semilinear Elliptic Problems

DOI10.1080/03605309908820681zbMath0708.35030OpenAlexW2030552694MaRDI QIDQ3490353

Miguel Escobedo, Julián Aguirre, Enrique Zuazua

Publication date: 1990

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309908820681

zbMATH Keywords

self-similar solutionsuniquenesspositive solutionconstraint

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Nonlinear elliptic equations (35J60) Generalized solutions to partial differential equations (35Dxx)

Related Items (17)

ON ZERO MASS SOLUTIONS OF VISCOUS CONSERVATION LAWS ⋮ On the blow-up of solutions of a convective reaction diffusion equation ⋮ Asymptotic behavior of solutions to the Burgers' equation with a nonlocal term ⋮ Existence of weak solutions to a convection-diffusion equation in amalgam spaces ⋮ Freezing similarity solutions in the multi-dimensional Burgers equation ⋮ A very singular solution and other self-similar solutions of the heat equation with convection ⋮ On Gaussian decay estimates of solutions to some linear elliptic equations and their applications ⋮ Stability of periodic stationary solutions of scalar conservation laws with space-periodic flux ⋮ Source-type solutions of heat equations with convection in several variables space ⋮ Large time behavior for convection-diffusion equations in \(\mathbb{R}{} ^ N\) ⋮ Self-similar solutions for a convection-diffusion equation with absorption in \({\mathbb{R}{}}^ N\) ⋮ Asymptotic behaviors of solutions to evolution equations in the presence of translation and scaling invariance ⋮ A splitting method for the augmented Burgers equation ⋮ Self-similarity and the singular Cauchy problem for the heat equation with cubic absorption ⋮ Long-time behavior for a nonlocal convection diffusion equation ⋮ Existence of weak solutions to a convection-diffusion equation in a uniformly local Lebesgue space ⋮ A Compactness Tool for the Analysis of Nonlocal Evolution Equations

Cites Work

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• Large time behaviour of solutions of the porous media equation with absorption
• Source-type solutions of degenerate diffusion equations with absorption
• Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus
• Generalized Burgers equations and Euler–Painlevé transcendents. I
• Variational problems related to self-similar solutions of the heat equation
• Resonance for jumping non-linearities.
• Some limit cases of L^p‐estimates for solutions of second order elliptic equations

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