scholarly journals EXISTENCE AND UNIQUENESS RESULTS, THE MARKOVIAN PROPERTY OF SOLUTION FOR A NEUTRAL DELAY STOCHASTIC REACTION-DIFFUSION EQUATION IN ENTIRE SPACE

2018 ◽  
Vol 28 (1) ◽  
Author(s):  
K.K. KENZHEBAEV ◽  
A.N. STANZHYTSKYI ◽  
A.O. TSUKANOVA
Keyword(s):  
Diffusion Equation ◽  
Existence And Uniqueness ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Entire Space ◽  
Neutral Delay ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Markovian Property ◽  
Stochastic Reaction

scholarly journals Regularity of a Stochastic Fractional Delayed Reaction-Diffusion Equation Driven by Lévy Noise

2013 ◽  
Vol 2013 ◽  
pp. 1-11
Author(s):  
Tianlong Shen ◽  
Jianhua Huang ◽  
Jin Li
Keyword(s):  
Fixed Point ◽  
Diffusion Equation ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Banach Fixed Point Theorem ◽  
Fractional Operator ◽  
Initial Value ◽  
Delayed Reaction

The current paper is devoted to the regularity of the mild solution for a stochastic fractional delayed reaction-diffusion equation driven by Lévy space-time white noise. By the Banach fixed point theorem, the existence and uniqueness of the mild solution are proved in the proper working function space which is affected by the delays. Furthermore, the time regularity and space regularity of the mild solution are established respectively. The main results show that both time regularity and space regularity of the mild solution depend on the regularity of initial value and the order of fractional operator. In particular, the time regularity is affected by the regularity of initial value with delays.

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

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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