Well-posedness results for a class of semilinear time-fractional diffusion equations

In this paper, we discuss an initial value problem for the semilinear time-fractional diffusion equation. The local well-posedness (existence and regularity) is presented when the source term satisfies a global Lipschitz condition. The unique continuation of solution and finite time blowup result ar...

Full description

Saved in:
Bibliographic Details
Published inZeitschrift für angewandte Mathematik und Physik Vol. 71; no. 5
Main Authors de Andrade, Bruno, Van Au, Vo, O’Regan, Donal, Tuan, Nguyen Huy
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2020
Springer Nature B.V
Subjects
Boundary value problems
Engineering
Lipschitz condition
Mathematical Methods in Physics
Theoretical and Applied Mechanics
Well posed problems
33E12
35K70
Nonlinear problem
26A33
44A20
Blowup
35B40
Fractional calculus
Well-posedness
Online AccessGet full text

Cover

More Information
Summary:In this paper, we discuss an initial value problem for the semilinear time-fractional diffusion equation. The local well-posedness (existence and regularity) is presented when the source term satisfies a global Lipschitz condition. The unique continuation of solution and finite time blowup result are presented when the reaction terms are logarithmic functions (local Lipschitz types).
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-020-01348-y