International Journal of Functional Analysis, Operator Theory and Applications
Volume 3, Issue 2, Pages 191 - 210
(December 2011)
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SUPNORM ESTIMATES FOR BOUNDED SOLUTIONS OF GENERAL ONE-DIMENSIONAL NONLINEAR DEGENERATE DIFFUSION EQUATIONS NOT IN DIVERGENCE FORM
Valéria C. Brum, Márcio V. Ferreira and Paulo R. Zingano
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Abstract:
We derive some basic estimates for supnorm values  of bounded weak solutions to general diffusion equations of the form
with given   constant,  bounded, and initial data  for some  Comparison arguments and energy estimates give
for all  where  and  Other related estimates are also discussed. |
| Keywords and phrases: degenerate parabolic equations, comparison principle, Cauchy problem, weak solutions, supnorm estimates, energy method, ultracontractivity bounds. |
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