Electronic Journal of Differential Equations,
Vol. 1995(1995), No. 02, pp. 1-16.

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

Author: Hans Engler (Georgetown Univ., Washington, D.C., USA)

Abstract: For quasilinear integrodifferential equations of the form
$$ u_t - a*A(u) = f\,,$$
 where $a$ is a scalar singular integral kernel that
behaves like $t^{-\alpha}$,  $1/2 \leq \alpha < 1$ 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.