Blow-up for a non-linear stable non-Gaussian process in fractional time

2021/09/11 by Soveny Solís, Solís, S., Vicente Vergara +1
Mathematics · #35B44 #35C15 (Primary) #35E05 #60J35 (Secondary) #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2109.05305

openalex publication_date 2021/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The behaviour of solutions for a non-linear diffusion problem is studied. A subordination principle is applied to obtain the variation of parameters formula in the sense of Volterra equations, which leads to the integral representation of a solution in terms of the fundamental solutions. This representation, the so-called mild solution, is used to investigate some properties about continuity and non-negativeness of solutions as well as to prove a Fujita type blow-up result. Fujita's critical exponent is established in terms of the parameters of the stable non-Gaussian process and a result for global solutions is given.

Citations

• Symmetric Stable Laws and Stable-Like Jump-Diffusions

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