Space-Fractional Diffusion Equation with Variable Coefficients: Well-posedness and Fourier Pseudospectral Approximation

2021 ◽  
Vol 87 (1) ◽  
Author(s):  
Xue-Yang Li ◽  
Ai-Guo Xiao
Keyword(s):  
Diffusion Equation ◽  
Fractional Diffusion ◽  
Variable Coefficients ◽  
Fractional Diffusion Equation ◽  
Well Posedness ◽  
Space Fractional Diffusion Equation ◽  
Fourier Pseudospectral

scholarly journals Well-posedness results and blow-up for a semi-linear time fractional diffusion equation with variable coefficients

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Vo Van Au ◽  
Jagdev Singh ◽  
Anh Tuan Nguyen
Keyword(s):  
Diffusion Equation ◽  
Blow Up ◽  
Linear Time ◽  
Unique Continuation ◽  
Fractional Diffusion ◽  
Variable Coefficients ◽  
Fractional Diffusion Equation ◽  
Well Posedness ◽  
Regularity Estimates ◽  
Logarithmic Functions

<p style='text-indent:20px;'>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.</p>

scholarly journals Numerical Solution of Fractional Diffusion Equation Model for Freezing in Finite Media

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
R. S. Damor ◽  
Sushil Kumar ◽  
A. K. Shukla
Keyword(s):  
Diffusion Equation ◽  
Interface Velocity ◽  
Biological Tissues ◽  
Fractional Diffusion ◽  
Equation Model ◽  
Fractional Diffusion Equation ◽  
Heat Transfer Analysis ◽  
Engineering Sciences ◽  
Space Fractional Diffusion Equation ◽  
Fractional Differential

Phase change problems play very important role in engineering sciences including casting of nuclear waste materials, vivo freezing of biological tissues, solar collectors and so forth. In present paper, we propose fractional diffusion equation model for alloy solidification. A transient heat transfer analysis is carried out to study the anomalous diffusion. Finite difference method is used to solve the fractional differential equation model. The temperature profiles, the motion of interface, and interface velocity have been evaluated for space fractional diffusion equation.

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