ABSTRACT
We study the global regularity of solutions of the homogeneous Dirichlet problem for the parabolic equation with variable nonlinearity
where p(x, t), are given functions of their arguments,
and
. Conditions on the data are found that guarantee the existence of a unique strong solution such that
and
. It is shown that if
with
, p and
are Hölder-continuous in
,
and
, then for every strong solution
with any
.
Notes
No potential conflict of interest was reported by the authors.
To the memory of Prof. Vasily Zhikov.