International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 485-496

Partial differential equations with piecewise constant delay

Joseph Wiener1 and Lokenath Debnath2

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 (IVP) are discussed for differential equations with piecewise constant argument (EPCA) 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 IVP for linear partial differential equations with piecewise constant delay by using integral transforms. Finally, an abstract Cauchy problem is discussed.