Smoothing for Nonlinear Parabolic Equations
with Nonlinear Boundary Conditions
by
Gisele Goldstein, LSU
JTB 110, 4:15pm Tuesday, February 20, 1996
Abstract
Of concern are parabolic problems on a finite time domain [0,T] with
spatial variable x in a domain $\Omega$ in n-dimensional Euclidean
space. The problem treats initial data u(x,0)=f(x) integrable in
$\Omega$. The objective is to find solutions u(x,t) which are bounded
for fixed T. Detailed estimates are obtained for the maximum norm of
u(x,t) in $\Omega$ and the Hilbert space norm of its t-derivative.
These estimates bound the norm in terms of f(x) and powers of 1/t,
for all dimensions n.
Requests for preprints and reprints: schmitt@math.utah.edu,
Reference: Gisele Goldstein.
This source can be found at http://www.math.utah.edu/research/