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Abstract We provide conditions implying finite-time blowup of positive weak solutions to the semilinear equation where and are constants, is the fractional power of the Laplacian, is a fractional Brownian… Click to show full abstract
Abstract We provide conditions implying finite-time blowup of positive weak solutions to the semilinear equation where and are constants, is the fractional power of the Laplacian, is a fractional Brownian motion with Hurst parameter H, and is a bounded measurable function. To achieve this we investigate the growth of integrals of the form as Moreover, we provide sufficient conditions for the existence of a global weak solution of the above equation, as well as upper and lower bounds for the probability that the solution does not blow up in finite time.
Journal Title: Stochastic Analysis and Applications
Year Published: 2020
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