Journal
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
Volume 518, Issue 1, Pages -Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmaa.2022.126682
Keywords
Stochastic Burgers-Huxley equation; Transition semigroup; Hamilton-Jacobi-Bellman equation; First variation equation
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Funding
- National Natural Science Foundation of China [11501325]
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This paper considers the transition semigroup related to the stochastic Burgers-Huxley equation, which describes the interaction between reaction mechanisms, convection effects, and diffusion transports. It is proved that the transition semigroup possesses a regularizing effect in the Banach space of continuous functions and some estimates on the derivative of the transition semigroup are established. An application in the Hamilton-Jacobi-Bellman equation arising from a stochastic optimal control problem is provided.
In this present paper we consider the transition semigroup {Pt}t & GE;0 related to the stochastic Burgers-Huxley equation which describes a prototype model for describing the interaction between reaction mechanisms, convection effects and diffusion transports. We are proving that it has a regularizing effect in the Banach space of continuous functions C(0, 1), that is, the transition semigroup {Pt}t & GE;0 possesses strong Feller property. Some estimates on derivative of the transition semigroup related to stochastic Burgers-Huxley equation are established based on the exponential moment estimates of the solution of stochastic Burgers-Huxley equation and its first variation equation. Finally, certain application in Hamilton-Jacobi-Bellman equation arising from stochastic optimal control problem is provided to illustrate our results.(c) 2022 Published by Elsevier Inc.
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