Elliptic regularizations for the nonlinear heat equation

The purpose of this paper is to study two elliptic regularizations for the nonlinear heat equation with nonlinear boundary conditions formulated below. Asymptotic expansions of the order zero for the solutions of these elliptic regularizations are established, including some boundary layer correctio...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-03, Vol.351 (1), p.392-399
Main Authors: Barbu, Luminiţa, Cosma, Emil
Format: Article
Language:English
Subjects:
Asymptotic expansions
Cauchy problems
Elliptic regularizations
Exact sciences and technology
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
Sciences and techniques of general use
Singular and regular perturbations
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Summary:The purpose of this paper is to study two elliptic regularizations for the nonlinear heat equation with nonlinear boundary conditions formulated below. Asymptotic expansions of the order zero for the solutions of these elliptic regularizations are established, including some boundary layer corrections. Under some appropriate smoothness and compatibility conditions on the data estimates for the remainder terms with respect to the C ( [ 0 , T ] ; L 2 ( Ω ) ) norm are proved in order to validate these expansions.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.10.033