Uniform Global Attractor for Nonautonomous Reaction–Diffusion Equations with Carathéodory’s Nonlinearity

2016 ◽  
pp. 265-272
Author(s):  
Nataliia V. Gorban ◽  
Liliia S. Paliichuk
Keyword(s):  
Global Attractor ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Uniform Global Attractor

scholarly journals Asymptotic gain results for attractors of semilinear systems

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Jochen Schmid ◽  
Oleksiy Kapustyan ◽  
Sergey Dashkovskiy
Keyword(s):  
Large Class ◽  
Global Attractor ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Practical Stability ◽  
Semilinear Systems ◽  
Nonlinear Reaction ◽  
Stability Results

<p style='text-indent:20px;'>We establish asymptotic gain along with input-to-state practical stability results for disturbed semilinear systems w.r.t. the global attractor of the respective undisturbed system. We apply our results to a large class of nonlinear reaction-diffusion equations comprising disturbed Chaffee–Infante equations, for example.</p>

scholarly journals Attractor of reaction-diffusion equations in Banach spaces

2001 ◽  
Vol 2 (1) ◽  
pp. 77
Author(s):  
José Valero
Keyword(s):  
Fractal Dimension ◽  
Phase Space ◽  
Banach Spaces ◽  
Global Attractor ◽  
Differential Inclusions ◽  
Reaction Diffusion ◽  
Global Attractors ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Dissipative Operators

In this paper we prove first some abstract theorems on existence of global attractors for differential inclusions generated by w-dissipative operators. Then these results are applied to reaction-diffusion equations in which the Babach space L<sub>p </sub>is used as phase space. Finally, new results concerning the fractal dimension of the global attractor in the space L<sub>2</sub> are obtained.<br /><sub> </sub>

scholarly journals Blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients under Neumann boundary conditions

2020 ◽  
Vol 18 (1) ◽  
pp. 1552-1564
Author(s):  
Huimin Tian ◽  
Lingling Zhang
Keyword(s):  
Boundary Conditions ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Nonlocal Reaction

Abstract In this paper, the blow-up analyses in nonlocal reaction diffusion equations with time-dependent coefficients are investigated under Neumann boundary conditions. By constructing some suitable auxiliary functions and using differential inequality techniques, we show some sufficient conditions to ensure that the solution u ( x , t ) u(x,t) blows up at a finite time under appropriate measure sense. Furthermore, an upper and a lower bound on blow-up time are derived under some appropriate assumptions. At last, two examples are presented to illustrate the application of our main results.

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