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.