International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 485-496
Partial differential equations with piecewise constant delay
1Department of Mathematics, The University of Texas - Pan American, Edinburg 78539, Texas, USA
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA
Received 25 October 1990; Revised 23 November 1990
Copyright © 1991 Joseph Wiener and Lokenath Debnath. 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.
The influence of certain discontinuous delays on the behavior of solutions to partial
differential equations is studied. In Section 2, the initial value problems () are discussed for differential
equations with piecewise constant argument () in partial derivatives. A class of loaded partial
differential equations that arise in solving certain inverse problems is studied in some detail in Section 3.
Section 4 is devoted to obtain the solutions of for linear partial differential equations with piecewise
constant delay by using integral transforms. Finally, an abstract Cauchy problem is discussed.