Existence and uniqueness of bounded weak solutions of a semilinear parabolic PDE

DOI10.1007/s10959-009-0252-4zbMath1205.60116OpenAlexW2090173696MaRDI QIDQ616266

Tu-Sheng Zhang, Qi-kang Ran

Publication date: 7 January 2011

Published in: Journal of Theoretical Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10959-009-0252-4

zbMATH Keywords

backward stochastic differential equationsquadratic growthbounded weak solutionssemilinear second-order parabolic equations

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Optimal stochastic control (93E20) Applications of stochastic analysis (to PDEs, etc.) (60H30) PDEs with randomness, stochastic partial differential equations (35R60)

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Cites Work

• Sobolev solution for semilinear PDE with obstacle under monotonicity condition
• Backward doubly stochastic differential equations and systems of quasilinear SPDEs
• Reflected solutions of backward SDE's, and related obstacle problems for PDE's
• Generalized BSDEs and nonlinear Neumann boundary value problems
• Reflected backward stochastic differential equation with jumps and random obstacle
• Solvability of backward stochastic differential equations with quadratic growth
• The smallest \(g\)-supermartingale and reflected BSDE with single and double \(L^2\) obstacles
• Generalized Reflected BSDE and an Obstacle Problem for PDEs with a Nonlinear Neumann Boundary Condition
• Probabilistic interpretation for systems of quasilinear parabolic partial differential equations
• Reflected backward stochastic differential equations under monotonicity and general increasing growth conditions
• Weak solutions for SPDE's and backward doubly stochastic differential equations
• Reflected forward-backward SDEs and obstacle problems with boundary conditions

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