On solutions of a system of hereditary and self-referred partial-differential equations. (English) Zbl 1202.35338
Summary: We present the local and global solutions of a system of hereditary and self-referred partial-differential equations. Namely, by the assumption on the Lipschitz continuity of the initial conditions \(u_0, v_0\), Theorem 1 states the existence of local solutions of the problem; furthermore, under the assumption that those initial conditions are non-negative, non-decreasing, bounded, and lower semi-continuous functions, Theorem 2 gives global solution which is also a non-negative, non-decreasing, bounded, and lower semi-continuous function (in variable \(x\) of even for any time \(t\)).
MSC:
35R10 | Partial functional-differential equations |
35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
35B09 | Positive solutions to PDEs |
45K05 | Integro-partial differential equations |
Keywords:
evolution equations; hereditary and self-referred differential equations; nonlinear integral equations; recursive schemeReferences:
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