Open AccessWell-posedness results and blow-up for a semi-linear time fractional diffusion equation with variable coefficients
Author(s) -
Vo Van Au,
Jagdev Singh,
Anh Tuấn Nguyễn
Publication year - 2021
Publication title -
electronic research archive
Language(s) - English
Resource type - Journals
ISSN - 2688-1594
DOI - 10.3934/era.2021052
Subject(s) - mathematics , uniqueness , lipschitz continuity , bessel function , mathematical analysis , logarithm , continuation , diffusion , diffusion equation , fractional calculus , physics , thermodynamics , economy , computer science , economics , programming language , service (business)
The semi-linear problem of a fractional diffusion equation with the Caputo-like counterpart of a hyper-Bessel differential is considered. The results on existence, uniqueness and regularity estimates (local well-posedness) of the solutions are established in the case of linear source and the source functions that satisfy the globally Lipschitz conditions. Moreover, we prove that the problem exists a unique positive solution. In addition, the unique continuation of solutions and a finite-time blow-up are proposed with the reaction terms are logarithmic functions.