scholarly journals Barenblatt solutions and asymptotic behaviour for a nonlinear fractional heat equation of porous medium type

2014 ◽  
Vol 16 (4) ◽  
pp. 769-803 ◽  
Author(s):  
Juan Vázquez
Keyword(s):  
Porous Medium ◽  
Heat Equation ◽  
Asymptotic Behaviour ◽  
Fractional Heat Equation ◽  
Medium Type

scholarly journals On the Lauwerier formulation of the temperature field problem in oil strata

2005 ◽  
Vol 2005 (10) ◽  
pp. 1577-1588 ◽  
Author(s):  
Lyubomir Boyadjiev ◽  
Ognian Kamenov ◽  
Shyam Kalla
Keyword(s):  
Porous Medium ◽  
Temperature Field ◽  
Boundary Value Problem ◽  
Heat Equation ◽  
Laplace Transform ◽  
Special Functions ◽  
Integral Form ◽  
Field Problem ◽  
Fractional Heat Equation ◽  
The Laplace Transform

The paper is concerned with the fractional extension of the Lauwerier formulation of the problem related to the temperature field description in a porous medium (sandstone) saturated with oil (strata). The boundary value problem for the fractional heat equation is solved by means of the Caputo differintegration operatorD∗(α)of order0<α≤1and the Laplace transform. The solution is obtained in an integral form, where the integrand is expressed in terms of a convolution of two special functions of Wright type.

scholarly journals Determination of source term for fractional heat equation on the sphere

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 361-370
Author(s):  
Nguyen Phuong ◽  
Tran Binh ◽  
Nguyen Luc ◽  
Nguyen Can
Keyword(s):  
Diffusion Equation ◽  
Heat Equation ◽  
Exact Solutions ◽  
Source Term ◽  
Fractional Diffusion ◽  
Inverse Source Problem ◽  
Fractional Heat Equation ◽  
Ill Posed ◽  
Time Fractional Diffusion Equation

In this work, we study a truncation method to solve a time fractional diffusion equation on the sphere of an inverse source problem which is ill-posed in the sense of Hadamard. Through some priori assumption, we present the error estimates between the regularized and exact solutions.

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