International Journal of Mathematics and Mathematical Sciences 
Volume 20 (1997), Issue 1, Pages 187-195
doi:10.1155/S0161171297000239

Boundary value problems for the diffusion equation with piecewise continuous time delay

Joseph Wiener1 and Lokenath Debnath2

 1Department of Mathematics, University of Texas - Pan American, Edinburg 78539, Texas, USA
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA
Received 30 November 1995; Revised 20 January 1996

Abstract

A study is made of partial differential equations with piecewise constant arguments. Boundary value problems for three types of equations are discussed delayed; alternately of advanced and retarded type; and most importantly, an equation of neutral type (that is, including the derivative at different values of time t).