Joseph Wiener, Lokenath Debnath, "Partial differential equations with piecewise constant delay", International Journal of Mathematics and Mathematical Sciences, vol. 14, Article ID 395172, 12 pages, 1991. https://doi.org/10.1155/S0161171291000674
Partial differential equations with piecewise constant delay
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.
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