On the existence of maximal and minimal solutions for parabolic partial differential equations
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- by J. W. Bebernes and K. Schmitt PDF
- Proc. Amer. Math. Soc. 73 (1979), 211-218 Request permission
Abstract:
The existence of maximal and minimal solutions for initial-boundary value problems and the Cauchy initial value problem associated with $Lu = f(x,t,u,\nabla u)$ where L is a second order uniformly parabolic differential operator is obtained by constructing maximal and minimal solutions from all possible lower and all possible upper solutions, respectively. This approach allows f to be highly nonlinear, i.e., f locally Hölder continuous with almost quadratic growth in $|\nabla u|$.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 211-218
- MSC: Primary 35K55
- DOI: https://doi.org/10.1090/S0002-9939-1979-0516467-3
- MathSciNet review: 516467