- Advances in the Theory of Nonlinear Analysis and its Application
- Vol: 6 Issue: 3
- Analytical studies on the global existence and blow-up of solutions for a free boundary problem of t...
Analytical studies on the global existence and blow-up of solutions for a free boundary problem of two-dimensional diffusion equations of moving fractional order
Authors : Rabah Djemiat, Bilal Basti, Noureddine Benhamidouche
Pages : 287-299
Doi:10.31197/atnaa.1031436
View : 4 | Download : 1
Publication Date : 2022-09-30
Article Type : Research
Abstract :This paper particularly addresses and discusses some analytical studies on the existence and uniqueness of global or blow-up solutions under the traveling profile forms for a free boundary problem of two-dimensional diffusion equations of moving fractional order. It does so by applying the properties of Schauder's and Banach's fixed point theorems. For application purposes, some examples of explicit solutions are provided to demonstrate the usefulness of our main results.Keywords : Fractional diffusion, moving fractional order, free boundary, blow-up, global existence, uniqueness