Jochen Merker
Abstract:
We prove under weak assumptions that solutions
of
doubly nonlinear reaction-diffusion equations
to initial values
are instantly regularized to functions
(ultracontractivity). Our proof is
based on a priori estimates of
for a time-dependent exponent
.
These a priori estimates can be obtained in an
elementary way from logarithmic Gagliardo-Nirenberg inequalities
by an optimal choice of
,
and they do not only imply
ultracontractivity, but provide further information about the
long-time behaviour.
Published April 15, 2009.
Math Subject Classifications: 35K65, 35B35, 46E35, 35B45.
Key Words: p-Laplacian; doubly nonlinear evolution equations;
ultracontractive semigroups;
logarithmic Gagliardo-Nirenberg inequalities.
Show me the PDF file (219 KB), TEX file, and other files for this article.
Jochen Merker University of Rostock, D-18051 Rostock, Germany email: jochen.merker@uni-rostock.de |
Return to the table of contents
for this conference.
Return to the EJDE web page