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Linear parabolic equations with singular potentials Herbert Amann
 

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
> =

  

Source: Amann, Herbert - Institut für Mathematik, Universität Zürich

 

Collections: Mathematics