Abstract volterra integrodifferential equations and a class of reaction-diffusion equations

1979 ◽  
pp. 295-303 ◽  
Author(s):  
G. F. Webb
Keyword(s):  
Reaction Diffusion ◽  
Integrodifferential Equations ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations

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

Global existence and asymptotic decay for systems of convective reaction-diffusion equations

1991 ◽  
Vol 17 (8) ◽  
pp. 725-739 ◽  
Author(s):  
Selwyn L. Hollis ◽  
Jeff Morgan
Keyword(s):  
Global Existence ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotic Decay

scholarly journals Characterization of Cocycle Attractors for Nonautonomous Reaction–Diffusion Equations

2016 ◽  
Vol 26 (08) ◽  
pp. 1650135 ◽  
Author(s):  
C. A. Cardoso ◽  
J. A. Langa ◽  
R. Obaya
Keyword(s):  
Chaotic Dynamics ◽  
Linear Part ◽  
Reaction Diffusion ◽  
Positive Cone ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Minimal Set ◽  
Full Characterization ◽  
The Stability

In this paper, we describe in detail the global and cocycle attractors related to nonautonomous scalar differential equations with diffusion. In particular, we investigate reaction–diffusion equations with almost-periodic coefficients. The associated semiflows are strongly monotone which allow us to give a full characterization of the cocycle attractor. We prove that, when the upper Lyapunov exponent associated to the linear part of the equations is positive, the flow is persistent in the positive cone, and we study the stability and the set of continuity points of the section of each minimal set in the global attractor for the skew product semiflow. We illustrate our result with some nontrivial examples showing the richness of the dynamics on this attractor, which in some situations shows internal chaotic dynamics in the Li–Yorke sense. We also include the sublinear and concave cases in order to go further in the characterization of the attractors, including, for instance, a nonautonomous version of the Chafee–Infante equation. In this last case we can show exponentially forward attraction to the cocycle (pullback) attractors in the positive cone of solutions.

ADER finite volume schemes for nonlinear reaction–diffusion equations

2009 ◽  
Vol 59 (1) ◽  
pp. 73-100 ◽  
Author(s):  
Eleuterio F. Toro ◽  
Arturo Hidalgo
Keyword(s):  
Finite Volume ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Finite Volume Schemes ◽  
Nonlinear Reaction
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