Large time behavior for convection-diffusion equations in irnwith asymptotically constant diffusion

DOI10.1080/03605309908821466zbMath0931.35068OpenAlexW1966500451MaRDI QIDQ4261545

Gema Duro, Enrique Zuazua

Publication date: 23 February 2000

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

Full work available at URL: https://doi.org/10.1080/03605309908821466

zbMATH Keywords

heat kernelasymptotically constant diffusionone-parameter family of self-similar solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Nonlinear parabolic equations (35K55) Initial value problems for second-order parabolic equations (35K15)

Related Items (20)

ON ZERO MASS SOLUTIONS OF VISCOUS CONSERVATION LAWS ⋮ ASYMPTOTIC EXPANSION FOR DAMPED WAVE EQUATIONS WITH PERIODIC COEFFICIENTS ⋮ Asymptotic expansions of solutions of the Cauchy problem for nonlinear parabolic equations ⋮ Large-time behaviour for anisotropic stable nonlocal diffusion problems with convection ⋮ The Brownian traveller on manifolds ⋮ The asymptotic behaviour of the heat equation in a twisted Dirichlet-Neumann waveguide ⋮ The improved decay rate for the heat semigroup with local magnetic field in the plane ⋮ Decay estimates for 1-D parabolic PDES with boundary disturbances ⋮ The Hardy inequality and the heat equation in twisted tubes ⋮ LINEAR PARABOLIC EQUATIONS IN LOCALLY UNIFORM SPACES ⋮ Asymptotic profiles for convection-diffusion equations with variable diffusion ⋮ Critical nonlinearity exponent and self-similar asymptotics for Lévy conservation laws ⋮ Large Time Behavior for a SimplifiedN-Dimensional Model of Fluid–Solid Interaction ⋮ Existence of weak solutions to a convection-diffusion equation in a uniformly local Lebesgue space ⋮ Some \(L^p\) estimates for rotationally invariant systems of viscous conservation laws ⋮ The asymptotic behaviour of the heat equation in a sheared unbounded strip ⋮ The Hardy inequality and the heat equation with magnetic field in any dimension ⋮ Large time behavior for convection-diffusion equations in \(\mathbb{R}^N\) with periodic coefficients ⋮ Asymptotic self-similarity in diffusion equations with nonconstant radial limits at infinity ⋮ Asymptotics for a nonlinear integral equation with a generalized heat kernel

Cites Work

• Large time asymptotics for fundamental solutions of diffusion equations
• Compact sets in the space \(L^ p(0,T;B)\)
• Large time behavior for convection-diffusion equations in \(\mathbb{R}{} ^ N\)
• Variational problems related to self-similar solutions of the heat equation
• Bounds for the fundamental solution of a parabolic equation
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