Nsoki Mavinga, Mubenga N. Nkashama
Abstract:
We are concerned with bounded solutions existing for all times for
nonlinear parabolic equations with possibly nonlinear boundary
conditions. A counterexample shows that, without an additional
condition, a (weak) maximum principle does not hold for linear
problems defined on the entire real line in time. We consider
solutions bounded for all times and derive a (weak) maximum
principle which is valid on the entire real line. Using comparison
techniques, a priori estimates and approximation methods, we
prove the existence and, in some cases, positivity and uniqueness of
bounded solutions existing for all times.
Published September 25, 2010.
Math Subject Classifications: 35K55, 35K60.
Key Words: Nonlinear parabolic equations; nonlinear boundary conditions;
sub and super-solutions; interpolation inequalities;
a priori estimates; bounded solutions.
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Nsoki Mavinga Department of Mathematics, University of Rochester Rochester, NY 14627-0138, USA email: mavinga@math.rochester.edu | |
Mubenga N. Nkashama Department of Mathematics, University of Alabama at Birmingham Birmingham, AL 35294-1170, USA email: nkashama@math.uab.edu |
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