scholarly journals Global solutions to quasilinear wave equations in homogeneous waveguides with Neumann boundary conditions

2012 ◽  
Vol 11 (2) ◽  
pp. 547-556
Author(s):  
Jason Metcalfe ◽  
◽  
Jacob Perry
Keyword(s):  
Boundary Conditions ◽  
Wave Equations ◽  
Global Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Quasilinear Wave Equations

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.

Immediate smoothing and global solutions for initial data in L1 × W1,2 in a Keller–Segel system with logistic terms in 2D

2020 ◽  
pp. 1-21
Author(s):  
Johannes Lankeit
Keyword(s):  
Initial Data ◽  
Boundary Conditions ◽  
Global Solutions ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Two Dimensional ◽  
Image Position

This paper deals with the logistic Keller–Segel model \[ \begin{cases} u_t = \Delta u - \chi \nabla\cdot(u\nabla v) + \kappa u - \mu u^2, \\ v_t = \Delta v - v + u \end{cases} \] in bounded two-dimensional domains (with homogeneous Neumann boundary conditions and for parameters χ, κ ∈ ℝ and μ > 0), and shows that any nonnegative initial data (u0, v0) ∈ L1 × W1,2 lead to global solutions that are smooth in $\bar {\Omega }\times (0,\infty )$ .

CONVERGENCE TO EQUILIBRIUM FOR A PARABOLIC–HYPERBOLIC PHASE-FIELD SYSTEM WITH NEUMANN BOUNDARY CONDITIONS

2007 ◽  
Vol 17 (01) ◽  
pp. 125-153 ◽  
Author(s):  
HAO WU ◽  
MAURIZIO GRASSELLI ◽  
SONGMU ZHENG
Keyword(s):  
Boundary Conditions ◽  
Type Inequality ◽  
Global Solutions ◽  
Neumann Boundary ◽  
Coupled System ◽  
Neumann Boundary Conditions ◽  
Convergence To Equilibrium ◽  
Relative Temperature ◽  
Real Analytic Functions ◽  
Phase Field System

This paper is concerned with the asymptotic behavior of global solutions to a parabolic–hyperbolic coupled system which describes the evolution of the relative temperature θ and the order parameter χ in a material subject to phase transitions. For the system with homogeneous Neumann boundary conditions for both ¸ and χ, under the assumption that the nonlinearities λ and ϕ are real analytic functions, we prove the convergence of a global solution to an equilibrium as time goes to infinity by means of a suitable Łojasiewicz–Simon type inequality.

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
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