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2008-17

Some new properties of biharmonic heat kernels

by Gazzola, F., Grunau, H.-Ch..


Series: 2008-17, Preprints

MSC:
35K30 Initial value problems for higher-order parabolic equations
35B50 Maximum principles

Abstract:
Contrary to the second order case, biharmonic heat kernels are sign-changing.
A deep knowledge of their behaviour
may however allow to prove positivity results for solutions of the Cauchy problem.
We establish further properties of
these kernels, we prove some Lorch-Szegö-type monotonicity results and we give
some hints on how to obtain
similar results for higher polyharmonic parabolic problems.

Keywords:
biharmonic parabolic equations, heat kernels

This paper was published in:
Nonlinear Analysis 70, 2965 - 2973 (2009)