On continuous dependence of solution of parabolic equations on coefficients

Article type: Research Article

Authors: Kim, Hyejin

Affiliations: Department of Mathematics, University of Maryland, College Park, MD 20742, USA. E-mail: mathjini@math.umd.edu

Abstract: It is well known that solutions of classical initial-boundary problems for second-order parabolic equations depend continuously on the coefficients if the coefficients converge to their limits in a strong enough topology. In case of one spatial variable, we consider the question of the weakest possible topology providing convergence of the solutions. The problem is closely related to weak convergence of corresponding diffusion processes. Continuous Markov processes corresponding to the Feller operators DvDu arise, in general, as limiting processes. Solutions of the parabolic equations converge, in general, to the solutions of corresponding initial-boundary problems for the limiting operator DvDu.

Keywords: weak convergence, generalized second-order differential operators, gluing conditions, narrow tubes, discontinuous coefficients

DOI: 10.3233/ASY-2009-0918

Journal: Asymptotic Analysis, vol. 62, no. 3-4, pp. 147-162, 2009