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arXiv · 1301.5795

Obstacle problem for semilinear parabolic equations with measure data

Tomasz Klimsiak·Andrzej Rozkosz
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Abstract

We consider the obstacle problem with two irregular reflecting barriers for the Cauchy-Dirichlet problem for semilinear parabolic equations with measure data. We prove the existence and uniqueness of renormalized solutions of the problem and well as results on approximation of the solutions by the penaliztion method. In the proofs we use probabilistic methods of the theory of Markov processes and the theory of backward stochastic differential equations.

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Tomasz Klimsiak, Andrzej Rozkosz. 2013-01-24. Obstacle problem for semilinear parabolic equations with measure data. https://doi.org/10.1007/s00028-014-0269-8

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