Stability of wave equations with nonlinear damping in the dirichlet and neumann boundary conditions

2005 ◽  
pp. 47-64
Author(s):  
I. Lasiecka
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Neumann Boundary ◽  
Nonlinear Damping ◽  
Neumann Boundary Conditions

Trend to spatial homogeneity for solutions to semilinear damped wave equations

1987 ◽  
Vol 105 (1) ◽  
pp. 117-126 ◽  
Author(s):  
J. Solà-Morales ◽  
M. València
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Lipschitz Constant ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Spatial Homogeneity ◽  
Homogeneous Solutions ◽  
Spatially Homogeneous ◽  
Image Position

SynopsisThe semilinear damped wave equationssubject to homogeneous Neumann boundary conditions, admit spatially homogeneous solutions (i.e. u(x, t) = u(t)). In order that every solution tends to a spatially homogeneous one, we look for conditions on the coefficients a and d, and on the Lipschitz constant of f with respect to u.

An energy-preserving algorithm for nonlinear Hamiltonian wave equations with Neumann boundary conditions

CALCOLO ◽  
2017 ◽  
Vol 54 (4) ◽  
pp. 1379-1402 ◽  
Author(s):  
Wei Shi ◽  
Kai Liu ◽  
Xinyuan Wu ◽  
Changying Liu
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions

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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