Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 2, Pages 147-160
On the parabolic potentials in degenerate-type heat equation
Department of Mathematics and Computer Science, San Jose State University, San Jose 95192, CA, USA
Received 1 August 1990; Revised 1 February 1991
Copyright © 1991 Igor Malyshev. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Using distributions theory technique we introduce parabolic
potentials for the heat equation with one time-dependent coefficient
(not everywhere positive and continuous) at the highest space-derivative, discuss their properties, and apply obtained results to three illustrative problems. Presented technique allows to deal with some equation
of the degenerate/mixed type.