A link between the cost of fast controls for the 1-D heat equation and the uniform controllability of a 1-D transport-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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On uniqueness for a rough transport–diffusion equation

Comptes Rendus Mathematique ◽

10.1016/j.crma.2016.05.003 ◽

2016 ◽

Vol 354 (8) ◽

pp. 804-807 ◽

Cited By ~ 4

Author(s):

Guillaume Lévy

Keyword(s):

Diffusion Equation ◽

Transport Diffusion

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A new difference scheme for time fractional heat equations based on the Crank-Nicholson method

Fractional Calculus and Applied Analysis ◽

10.2478/s13540-013-0055-2 ◽

2013 ◽

Vol 16 (4) ◽

Cited By ~ 19

Author(s):

Ibrahim Karatay ◽

Nurdane Kale ◽

Serife Bayramoglu

Keyword(s):

Diffusion Equation ◽

Heat Equation ◽

Difference Scheme ◽

Numerical Solution ◽

Caputo Derivative ◽

Numerical Experiments ◽

Time Derivative ◽

Heat Equations ◽

First Order ◽

Fractional Heat Equation

AbstractIn this paper, we consider the numerical solution of a time-fractional heat equation, which is obtained from the standard diffusion equation by replacing the first-order time derivative with the Caputo derivative of order α, where 0 < α < 1. The main purpose of this work is to extend the idea on the Crank-Nicholson method to the time-fractional heat equations. By the method of the Fourier analysis, we prove that the proposed method is stable and the numerical solution converges to the exact one with the order O(τ 2-α + h 2), conditionally. Numerical experiments are carried out to support the theoretical claims.

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The cost of the control in the case of a minimal time of control: The example of the one-dimensional heat equation

Journal of Mathematical Analysis and Applications ◽

10.1016/j.jmaa.2017.01.096 ◽

2017 ◽

Vol 451 (1) ◽

pp. 497-507 ◽

Cited By ~ 3

Author(s):

Pierre Lissy

Keyword(s):

Heat Equation ◽

One Dimensional ◽

Minimal Time ◽

The One ◽

The Cost

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Invariant Solutions for Nonhomogeneous Discrete Diffusion Equation

Discrete Dynamics in Nature and Society ◽

10.1155/2013/146976 ◽

2013 ◽

Vol 2013 ◽

pp. 1-7

Author(s):

M. N. Qureshi ◽

A. Q. Khan ◽

M. Ayub ◽

Q. Din

Keyword(s):

Diffusion Equation ◽

Heat Equation ◽

Symmetry Algebra ◽

Invariant Solutions ◽

Source Terms ◽

One Dimensional

One-dimensional optimal systems for nonhomogeneous discrete heat equation with different source terms are calculated. By utilizing these optimal systems invariant solutions are found. Also generating solutions are calculated, using the elements of the symmetry algebra.

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Existence and Uniqueness of Weak Solution for chemotaxis model coupled with heat equation

10.22541/au.161756835.51485468/v1 ◽

2021 ◽

Author(s):

Ali slimani ◽

Amar Guesmia

Keyword(s):

Weak Solution ◽

Diffusion Equation ◽

Heat Equation ◽

Existence And Uniqueness ◽

Reaction Diffusion ◽

Reaction Diffusion Equation ◽

Chemical Concentration ◽

Chemotaxis Model ◽

Convection Diffusion Equation ◽

Global Existence And Uniqueness

Keller-Segel chemotaxis model is described by a system of nonlinear PDE : a convection diffusion equation for the cell density coupled with a reaction-diffusion equation for chemoattractant concentration. In this work, we study the phenomenon of Keller Segel model coupled with a heat equation, because The heat has an effect the density of the cells as well as the signal of chemical concentration, since the heat is a factor affecting the spread and attraction of cells as well in relation to the signal of chemical concentration, The main objectives of this work is the study of the global existence and uniqueness and boundedness of the weak solution for the problem defined in (8) for this we use the technical of Galerkin method.

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