scholarly journals A note on the axisymmetric diffusion equation

2021 ◽  
Vol 63 ◽  
pp. 333-341
Author(s):  
Alexander Patkowski
Keyword(s):  
Diffusion Equation ◽  
Explicit Solution ◽  
Inversion Formula ◽  
Residue Theorem

We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for \(u(r,t)\) as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as a rapidly converging series.   doi:10.1017/S1446181121000110

scholarly journals A NOTE ON THE AXISYMMETRIC DIFFUSION EQUATION

2021 ◽  
pp. 1-9
Author(s):  
ALEXANDER E. PATKOWSKI
Keyword(s):  
Diffusion Equation ◽  
Explicit Solution ◽  
Inversion Formula ◽  
Residue Theorem

Abstract We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for $u(r,t)$ as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as a rapidly converging series.

Generalized fraction evolution equations with fractional Gross Laplacian

2016 ◽  
Vol 19 (2) ◽  
Author(s):  
Samah Horrigue ◽  
Habib Ouerdiane ◽  
Imen Salhi
Keyword(s):  
Diffusion Equation ◽  
Laplace Transform ◽  
Explicit Solution ◽  
Evolution Equations ◽  
Fractional Diffusion ◽  
Generalized Function ◽  
Initial Condition ◽  
Infinite Dimensions ◽  
The Laplace Transform ◽  
Time Fractional Diffusion Equation

AbstractIn this paper, we define and consider the fractional Gross Laplacian which is characterized by the Laplace transform. As application, we study the generalized Riemann-Liouville time fractional diffusion equation in infinite dimensions. We show that the explicit solution is given as the convolution between the initial condition and a generalized function related to the Mittag-Leffler function.

PARTIAL HOMOGENIZATION OF THE DIFFUSION EQUATION WITH A DIRAC-LIKE POTENTIAL

2020 ◽  
Vol 18 (5) ◽  
pp. 507-518
Author(s):  
Latifa Ait Mahiout ◽  
Gregory P. Panasenko ◽  
Vitaly Volpert
Keyword(s):  
Diffusion Equation
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