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On global existence and blowup of solutions of stochastic Keller-Segel type equation. (English) Zbl 1479.35146

Summary: In this paper we consider a stochastic Keller-Segel type equation, perturbed with random noise. We establish that for special types of random pertubations (i.e. in a divergence form), the equation has a global weak solution for small initial data. Furthermore, if the noise is not in a divergence form, we show that the solution has a finite time blowup (with nonzero probability) for any nonzero initial data. The results on the continuous dependence of solutions on the small random perturbations, alongside with the existence of local strong solutions, are also derived in this work.

MSC:

35B44 Blow-up in context of PDEs
35K15 Initial value problems for second-order parabolic equations
35K59 Quasilinear parabolic equations
35R60 PDEs with randomness, stochastic partial differential equations
60H30 Applications of stochastic analysis (to PDEs, etc.)
65M75 Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs
92C17 Cell movement (chemotaxis, etc.)
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References:

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