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Viscosity solutions of fully nonlinear parabolic systems |
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| Authors: | Weian Liu Yin Yang |
| Affiliation: | a School of Mathematics and Statistics, Wuhan University, Wuhan, Hubei 430072, PR China b Department of Applied Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, PR China c Department of Mathematics, Central China Normal University, Wuhan, Hubei 430079, PR China |
| Abstract: | In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second-order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in Proc. London Math. Soc. 63 (1991) 212-240 and Comm. Partial Differential Equations 16 (1991) 1095-1128. |
| Keywords: | Viscosity solutions Systems of partial differential equations Fully nonlinear degenerate parabolic equations Perron's method Coupled solution |
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