Existence and Uniqueness of Bounded Weak Solutions of a Semilinear Parabolic PDE

Qikang Ran () and Tusheng Zhang ()
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Qikang Ran: Shanghai University of Finance and Economics
Tusheng Zhang: University of Manchester

Journal of Theoretical Probability, 2010, vol. 23, issue 4, 951-971

Abstract: 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.

Keywords: Semilinear second-order parabolic equations; Backward stochastic differential equations; Quadratic growth; Bounded weak solutions; 60H10; 35D05; 60H30B; 93E20; 35R60 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s10959-009-0252-4

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