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Global analysis of the shadow Gierer-Meinhardt system with general linear boundary conditions in a random environment. (English) Zbl 1466.60125

Summary: The global analysis of the shadow Gierer-Meinhardt system with multiplicative white noise and general linear boundary conditions is investigated in this paper. For this reaction-diffusion system, we employ a fixed point argument to prove local existence and uniqueness. Our results on global existence are based on a priori estimates of solutions.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H30 Applications of stochastic analysis (to PDEs, etc.)
35K51 Initial-boundary value problems for second-order parabolic systems
35R60 PDEs with randomness, stochastic partial differential equations
60H40 White noise theory
35K57 Reaction-diffusion equations
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References:

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