International Journal of Mathematics and Mathematical Sciences 
Volume 14 (1991), Issue 3, Pages 485-496
doi:10.1155/S0161171291000674

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

Abstract

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.