Electron. J. Diff. Eqns., Vol. 1995(1995), No. 02, pp. 1-16.

Strong Solutions of Quasilinear Integrodifferential Equations with Singular Kernels in Several Space Dimensions

Hans Engler

For quasilinear integrodifferential 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 $ less than 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.

Submitted December 15, 1994. Published February 24, 1995.
Math Subject Classification: 45K05 Key words: Integro-differential equation, strong solution, singular kernel, quasilinear.

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Hans Engler
Department of Mathematics, Georgetown University
Washington, D.C. 20057, USA
e-mail: engler@guvax.acc.georgetown.edu
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