A Neumann problem for a convection-diffusion equation on the half-line

Piotr Biler; Grzegorz Karch

ArticleOriginal scientific text

Title

A Neumann problem for a convection-diffusion equation on the half-line

Authors ¹, ¹

Affiliations

Mathematical Institute, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Abstract

We study solutions to a nonlinear parabolic convection-diffusion equation on the half-line with the Neumann condition at x=0. The analysis is based on the properties of self-similar solutions to that problem.

Keywords

ENG

Neumann problem, asymptotics of solutions., convection-diffusion equation

H. Brezis, L. A. Peletier and D. Terman, A very singular solution of the heat equation with absorption, Arch. Rational Mech. Anal. 95 (1986), 185-209.
S. Claudi, Asymptotic behaviour for a diffusion-convection equation with rapidly decreasing initial data, Adv. Differential Equations 3 (1998), 361-386.
S. Claudi and F. R. Guarguaglini, Large time behavior for the heat equation with absorption and convection, Adv. Appl. Math. 16 (1995), 377-401.
S. Claudi, R. Natalini and A. Tesei, Large time behaviour of a diffusion equation with strong convection, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1994), 445-474.
M. Escobedo, J. L. Vázquez and E. Zuazua, Asymptotic behaviour and source-type solutions for a diffusion-convection equation, Arch. Rational Mech. Anal. 124 (1993), 43-65.
M. Escobedo, J. L. Vázquez and E. Zuazua, A diffusion-convection equation in several space dimensions, Indiana Univ. Math. J. 42 (1993), 1413-1440.
M. Escobedo and E. Zuazua, Large time behavior for convection-diffusion equations in $f R^{N}$ , J. Funct. Anal. 100 (1991), 119-161.
M. Guedda, Self-similar solutions to a convection-diffusion process, Electron. J. Qual. Theory Differ. Equ. 2000, no. 3, 17 pp.
L. Herraiz, Asymptotic behaviour of solutions of some semilinear parabolic problems, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), 49-105.
S. Kaplan, On the growth of solutions of quasi-linear parabolic equations, Comm. Pure Appl. Math. 16 (1963), 305-330.
G. Karch, Large-time behavior of solutions to nonlinear wave equations: higher-order asymptotics, Math. Methods Appl. Sci. 22 (1999), 1671-1697.
G. Karch, Asymptotics of solutions to a convection-diffusion equation on the half-line, Proc. Roy. Soc. Edinburgh Sect. A 130 (2000), 837-853. \eject
L. A. Peletier and H. C. Serafini, A very singular solution and other self-similar solutions of the heat equation with convection, Nonlinear Anal. 24 (1995), 29-49.

Title

A Neumann problem for a convection-diffusion equation on the half-line

Affiliations

Abstract

Keywords

Bibliography