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Application of Rothe’s method to some functional differential equations with Dirichlet boundary conditions. (English) Zbl 1476.35291

Summary: The existence and uniqueness of a strong solution for a class of partial functional differential equations with Dirichlet boundary conditions is established by applying Rothe’s method. As an application, we included an example to illustrate the main result.

MSC:

35R10 Partial functional-differential equations
35K20 Initial-boundary value problems for second-order parabolic equations
35D35 Strong solutions to PDEs
47D06 One-parameter semigroups and linear evolution equations
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