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Summary: Linear parabolic equations with singular potentials
Herbert Amann
In memoriam Philippe Benilan
Abstract. By means of maximal regularity techniques we study the solvability of a linear
heat equation with a time-dependent potential under minimal regularity assumptions.
1. Introduction
Let
be a bounded smooth domain in R n with n 3. Set := @ x a positive
number T , and put J := (0; T ). Suppose that a is a time-dependent function on
a `potential', and consider the initial boundary value problem
@ t u u + au = 0
in
J;
u = 0 on J;
u(; 0) = u 0
on
:
9
> =
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