A family of integral representations for the solution of the diffusion equation

1975 ◽  
pp. 146-150
Author(s):  
James A. Donaldson
Keyword(s):  
Diffusion Equation ◽  
Integral Representations

scholarly journals ASSESSMENT OF GEOECOLOGICAL CONSEQUENCES OF SUBDUCTION PROCESSES

2021 ◽  
Vol 1 (6) ◽  
pp. 79-83
Author(s):  
M.V. Zaretskaya ◽  
◽  
V.V. Lozovoy ◽  
Keyword(s):  
Diffusion Equation ◽  
Volcanic Activity ◽  
Model Problem ◽  
Block Structure ◽  
Three Dimensional ◽  
Factorization Method ◽  
Integral Representations ◽  
Transport And Diffusion ◽  
Numerical Analytical Method ◽  
And Diffusion

t. The aim of the work is to develop a numerical-analytical method for assessing the geoecological consequences of volcanic activity accompanying the subduction process. The boundary problem was formulated, including the three-dimensional transport and diffusion equation and boundary conditions at the bottom and surface of the water. For research, a block structure with quasi-homogeneous layers is introduced. In each block, a differential factorization method is implemented and integral representations of solutions are obtained. Calculations for a model problem are carried out, conclusions are formulated about the features of the behavior of the heavy and light fractions of volcanic ejections depending on the speed of currents, intensity and duration of the eruption.

scholarly journals Subordination Approach to Space-Time Fractional Diffusion

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 415 ◽  
Author(s):  
Emilia Bazhlekova ◽  
Ivan Bazhlekov
Keyword(s):  
Fundamental Solution ◽  
Diffusion Equation ◽  
Numerical Evaluation ◽  
Dimensional Space ◽  
Gaussian Function ◽  
Fractional Diffusion ◽  
Space Time ◽  
Integral Representations ◽  
Dimensional Space Time ◽  
Time Fractional Diffusion Equation

The fundamental solution to the multi-dimensional space-time fractional diffusion equation is studied by applying the subordination principle, which provides a relation to the classical Gaussian function. Integral representations in terms of Mittag-Leffler functions are derived for the fundamental solution and the subordination kernel. The obtained integral representations are used for numerical evaluation of the fundamental solution for different values of the parameters.

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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