scholarly journals A variational approach to bifurcation points of a reaction-diffusion system with obstacles and neumann boundary conditions

2016 ◽  
Vol 61 (1) ◽  
pp. 1-25 ◽  
Author(s):  
Jan Eisner ◽  
Milan Kučera ◽  
Martin Väth
Keyword(s):  
Boundary Conditions ◽  
Variational Approach ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Bifurcation Points

Multiresolution wavelet bases with augmentation method for solving singularly perturbed reaction–diffusion Neumann problem

2019 ◽  
Vol 17 (01) ◽  
pp. 1850064
Author(s):  
Somlak Utudee ◽  
Montri Maleewong
Keyword(s):  
Boundary Conditions ◽  
Variational Approach ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Original System ◽  
Neumann Boundary Conditions ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Wavelet Bases ◽  
Numerical Examples

This paper developed the anti-derivative wavelet bases to handle the more general types of boundary conditions: Dirichlet, mixed and Neumann boundary conditions. The boundary value problem can be formulated by the variational approach, resulting in a system involving unknown wavelet coefficients. The wavelet bases are constructed to solve the unknown solutions corresponding to the types of solution spaces. The augmentation method is presented to reduce the dimension of the original system, while the convergence rate is in the same order as the multiresolution method. Some numerical examples have been shown to confirm the rate of convergence. The examples of the singularly perturbed problem with Neumann boundary conditions are also demonstrated, including highly oscillating cases.

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.

The Phenomenon of Quenching for a Reaction-Diffusion System with Non-Linear Boundary Conditions

2021 ◽  
Vol 88 (1-2) ◽  
pp. 155
Author(s):  
Halima Nachid ◽  
F. N'Gohisse ◽  
N'Guessan Koffi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Lower And Upper Bounds ◽  
Linear Reaction ◽  
The One ◽  
Quenching Time

We study the quenching behavior of the solution of a semi- linear reaction-diffusion system with nonlinear boundary conditions. We prove that the solution quenches in finite time and its quenching time goes to the one of the solution of the differential system. We also obtain lower and upper bounds for quenching time of the solution.

Global Existence and Blow-Up in Finite Time of Solutions to One Kind of Reaction-Diffusion Educations with Neumann Boundary Conditions

2014 ◽  
Vol 971-973 ◽  
pp. 1017-1020
Author(s):  
Jun Zhou Shao ◽  
Ji Jun Xu
Keyword(s):  
Global Existence ◽  
Boundary Conditions ◽  
Finite Time ◽  
Blow Up ◽  
Neumann Boundary ◽  
Reaction Diffusion ◽  
Neumann Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Blowing Up ◽  
Processing Techniques

This paper deals with the properties of one kind of reaction-diffusion equations with Neumann boundary conditions based on the comparison principles. The relations of parameter and the situation of the coupled about equations are used to construct the global existent super-solutions and the blowing-up sub-solutions, and then we obtain the conditions of the global existence and blow-up in finite time solutions with the processing techniques of inequality.

Sign in / Sign up

Export Citation Format

Share Document