Existence of solutions to the slow diffusion equation with a nonlinear source

2020 ◽  
Vol 484 (2) ◽  
pp. 123721
Author(s):  
Ryuichi Sato
Keyword(s):  
Diffusion Equation ◽  
Existence Of Solutions ◽  
Nonlinear Source ◽  
Slow Diffusion ◽  
Slow Diffusion Equation

scholarly journals Lower Bounds Estimate for the Blow-Up Time of a Slow Diffusion Equation with Nonlocal Source and Inner Absorption

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Zhong Bo Fang ◽  
Rui Yang ◽  
Yan Chai
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Lower Bounds ◽  
Blow Up ◽  
Neumann Boundary ◽  
Nonlocal Source ◽  
Slow Diffusion ◽  
Homogeneous Neumann Boundary Condition ◽  
Inner Absorption ◽  
Slow Diffusion Equation

We investigate a slow diffusion equation with nonlocal source and inner absorption subject to homogeneous Dirichlet boundary condition or homogeneous Neumann boundary condition. Based on an auxiliary function method and a differential inequality technique, lower bounds for the blow-up time are given if the blow-up occurs in finite time.

scholarly journals Global null controllability of the 1-dimensional nonlinear slow diffusion equation

2013 ◽  
Vol 34 (3) ◽  
pp. 333-344 ◽  
Author(s):  
Jean-Michel Coron ◽  
Jesús Ildefonso Díaz ◽  
Abdelmalek Drici ◽  
Tommaso Mingazzini
Keyword(s):  
Diffusion Equation ◽  
Null Controllability ◽  
Slow Diffusion ◽  
Slow Diffusion Equation

Stepwise regularization method for a nonlinear Riesz–Feller space-fractional backward diffusion problem

2019 ◽  
Vol 27 (6) ◽  
pp. 759-775
Author(s):  
Dang Duc Trong ◽  
Dinh Nguyen Duy Hai ◽  
Nguyen Dang Minh
Keyword(s):  
Exact Solution ◽  
Initial Data ◽  
Diffusion Equation ◽  
Regularization Method ◽  
Fractional Diffusion ◽  
Diffusion Problem ◽  
Convergence Estimate ◽  
Nonlinear Source ◽  
Space Fractional Diffusion Equation ◽  
Final Data

Abstract In this paper, we consider the backward diffusion problem for a space-fractional diffusion equation (SFDE) with a nonlinear source, that is, to determine the initial data from a noisy final data. Very recently, some papers propose new modified regularization solutions to solve this problem. To get a convergence estimate, they required some strongly smooth conditions on the exact solution. In this paper, we shall release the strongly smooth conditions and introduce a stepwise regularization method to solve the backward diffusion problem. A numerical example is presented to illustrate our theoretical result.

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