International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 1, Pages 187-195

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

Copyright © 1997 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.


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).