Uniform attractors for the non-autonomous reaction-diffusion equations with delays

2020 ◽  
pp. 1-26
Author(s):  
Kaixuan Zhu ◽  
Yongqin Xie ◽  
Feng Zhou ◽  
Xin Li
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Uniform Attractors

The existence of uniform attractors for non-autonomous reaction-diffusion equations on the whole space

2012 ◽  
Vol 53 (8) ◽  
pp. 082703 ◽  
Author(s):  
Yongqin Xie ◽  
Kaixuan Zhu ◽  
Chunyou Sun
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Whole Space ◽  
Uniform Attractors

Uniform attractors for impulsive reaction–diffusion equations

2010 ◽  
Vol 216 (9) ◽  
pp. 2534-2543 ◽  
Author(s):  
Xingjie Yan ◽  
Ying Wu ◽  
Chengkui Zhong
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Uniform Attractors ◽  
Impulsive Reaction

Uniform attractors for reaction–diffusion equations with a larger class of external forces

2022 ◽  
Vol 63 (1) ◽  
pp. 011508
Author(s):  
Xiangming Zhu ◽  
Chengkui Zhong
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Uniform Attractors ◽  
External Forces

scholarly journals Uniform attractors for nonautonomous reaction-diffusion equations with the nonlinearity in a larger symbol space

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xiangming Zhu ◽  
Chengkui Zhong
Keyword(s):  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Uniform Attractor ◽  
Symbol Space ◽  
Uniform Attractors

<p style='text-indent:20px;'>Existence and structure of the uniform attractors for reaction-diffusion equations with the nonlinearity in a weaker topology space are considered. Firstly, a weaker symbol space is defined and an example is given as well, showing that the compactness can be easier obtained in this space. Then the existence of solutions with new symbols is presented. Finally, the existence and structure of the uniform attractor are obtained by proving the <inline-formula><tex-math id="M1">\begin{document}$ (L^{2}\times \Sigma, L^{2}) $\end{document}</tex-math></inline-formula>-continuity of the processes generated by solutions.</p>

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.

scholarly journals Pointwise nonlinear scaling for reaction–diffusion equations

2009 ◽  
Vol 59 (8) ◽  
pp. 1858-1869 ◽  
Author(s):  
Martin Weiser
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations

scholarly journals Input-to-state stability results w.r.t. global attractors of semi-linear reaction-diffusion equations

2020 ◽  
Vol 53 (2) ◽  
pp. 3186-3191
Author(s):  
Sergey Dashkovskiy ◽  
Oleksiy Kapustyan ◽  
Jochen Schmid
Keyword(s):  
Reaction Diffusion ◽  
Global Attractors ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Linear Reaction ◽  
Stability Results
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