Existence and Uniqueness of Bounded Weak Solutions of a Semilinear Parabolic PDE |
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Authors: | Qikang Ran Tusheng Zhang |
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Affiliation: | 1.Department of Applied Mathematics,Shanghai University of Finance and Economics,Shanghai,China;2.School of Mathematics,University of Manchester,Manchester,UK |
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Abstract: | This paper has two parts. In part I, the existence and uniqueness are established for Sobolev solutions of a class of semilinear parabolic partial differential equations. Moreover, a probabilistic interpretation of the solutions in terms of backward stochastic differential equations is obtained. In part II, the existence for viscosity solutions of PDEs with obstacle and Neumann boundary condition is proved. |
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