Non-existence of solutions for a non-Gaussian equation in fractional time with Osgood type nonlinearity

2024/05/21 by Soveny Solís, Solís, Soveny, Vicente Vergara +1 · 1 citation
Engineering · Mathematics · #35B33 #35C15 #47A52 #AMS subject classification: 35B44 (primary) #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2405.13151

openalex publication_date 2024/05/21 · openalex created_date 2024/05/25 · openalex updated_date 2026/07/28

Abstract

Osgood functions in the source term are used to produce results for non-existence of local solutions into the framework of non-Gaussian diffusion equations. The critical exponent for non-existence of local solutions is found to depend on the fractional derivative, the non-Gaussian diffusion and the non-linear term. The instantaneous blow-up phenomenon is studied by exploiting estimates of the fundamental solutions. Nevertheless, theory of super-solutions and fixed points are combined for showing existence of global solutions. In this case, the critical exponent for existence of global solutions depends only on the last two parameters above.

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