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

Author

Listed:
  • Qikang Ran

    (Shanghai University of Finance and Economics)

  • Tusheng Zhang

    (University of Manchester)

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.

Suggested Citation

  • Qikang Ran & Tusheng Zhang, 2010. "Existence and Uniqueness of Bounded Weak Solutions of a Semilinear Parabolic PDE," Journal of Theoretical Probability, Springer, vol. 23(4), pages 951-971, December.
    • Handle: RePEc:spr:jotpro:v:23:y:2010:i:4:d:10.1007_s10959-009-0252-4
    DOI: 10.1007/s10959-009-0252-4
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    References listed on IDEAS

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    1. V. Bally & A. Matoussi, 2001. "Weak Solutions for SPDEs and Backward Doubly Stochastic Differential Equations," Journal of Theoretical Probability, Springer, vol. 14(1), pages 125-164, January.
    2. Jin Ma & Jakša Cvitanić, 2001. "Reflected forward-backward SDE s and obstacle problems with boundary conditions," International Journal of Stochastic Analysis, Hindawi, vol. 14, pages 1-26, January.
    3. Tevzadze, Revaz, 2008. "Solvability of backward stochastic differential equations with quadratic growth," Stochastic Processes and their Applications, Elsevier, vol. 118(3), pages 503-515, March.
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