Partial functional differential equation with an integral condition and applications to population dynamics. (English) Zbl 1155.35478
Summary: We consider a semilinear functional partial differential equation with an integral condition. We apply the method of semidiscretization in time, to establish the existence and uniqueness of solutions. We also study the continuation of the solution to the maximal interval of existence. Finally we give examples to demonstrate the applications of our results.
MSC:
| 35R10 | Partial functional-differential equations |
| 92D25 | Population dynamics (general) |
| 35A05 | General existence and uniqueness theorems (PDE) (MSC2000) |
| 35B60 | Continuation and prolongation of solutions to PDEs |
Keywords:
diffusion equation; retarded argument; weak solution; method of lines; continuation of solutionsReferences:
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