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Strong solutions of quasilinear integro-differential equations with singular kernels in several space dimensions. (English) Zbl 0813.45004

For quasilinear integro-differential equations of the form \(u_ t - a^* A(u) = f\), where \(a\) is a scalar singular integral kernel that behaves like \(t^{-\alpha}\), \(1/2 \leq \alpha < 1\) and \(A\) is a second order quasilinear elliptic operator in divergence form, solutions are found for which \(A(u)\) is integrable over space and time.
Reviewer: H.Engler

MSC:

45K05 Integro-partial differential equations
45G05 Singular nonlinear integral equations
Full Text: EuDML EMIS