Journal of Applied Mathematics and Stochastic Analysis
Volume 4 (1991), Issue 2, Pages 147-160

On the parabolic potentials in degenerate-type heat equation

Igor Malyshev

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.