Global Nonexistence of Positive Initial-Energy Solutions for Coupled Nonlinear Wave Equations with Damping and Source Terms
- Global Well-Posedness for the Generalized Large-Scale Semigeostrophic Equations. Çalik, Mahmut; Oliver, Marcel; Vasylkevych, Sergiy // Archive for Rational Mechanics & Analysis;Mar2013, Vol. 207 Issue 3, p969
We prove existence and uniqueness of global classical solutions to the generalized large-scale semigeostrophic equations with periodic boundary conditions. This family of Hamiltonian balance models for rapidly rotating shallow water includes the L model derived by R. Salmon in 1985 and its 2006...
- Blow up of positive initial-energy solutions to systems of nonlinear wave equations with degenerate damping and source terms. BENAISSA, Abbes; OUCHENANE, Djamel; ZENNIR, Khaled // Nonlinear Studies;2012, Vol. 19 Issue 4, p523
Blow up of solutions to systems of nonlinear wave equations with degenerate damping and source terms supplemented with the initial and Dirichlet boundary conditions is shown in , in a bounded domain O ? Rn, where n = 1,2,3 and the initial energy is negative. Our result extends this previous...
- Growth of Solutions with Positive Initial Energy to Systems of Nonlinear Wave Equations with Damping and Source Terms. Pişkin, Erhan // Advances in Mathematical Physics;2/22/2015, Vol. 2015, p1
We consider initial-boundary conditions for coupled nonlinear wave equations with damping and source terms. We prove that the solutions of the problem are unbounded when the initial data are large enough in some sense.
- Global existence, decay and blow up solutions for coupled nonlinear wave equations with damping and source terms. PİŞKİN, Erhan; POLAT, Necat // Turkish Journal of Mathematics;Jul2013, Vol. 37 Issue 3, p633
We study the initial-boundary value problem for a system of nonlinear wave equations with nonlinear damping and source terms, in a bounded domain. The decay estimates of the energy function are established by using Nakao's inequality. The nonexistence of global solutions is discussed under some...
- Existence of time periodic solutions for a damped generalized coupled nonlinear wave equations. Fang Shao-mei; Guo Bo-ling // Applied Mathematics & Mechanics;Jun2003, Vol. 24 Issue 6, p673
The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied. By using the Galerkin method to construct the approximating sequence of time periodic solutions, a priori estimate and Laray-Schauder fixed point theorem to...
- A semilinear wave equation with space-time dependent coefficients and a memory boundarylike antiperiodic condition: Regularity and stability. Lê, Út V. // Journal of Mathematical Physics;Oct2010, Vol. 51 Issue 10, p103504
This paper deals with regularity and stability of solutions to an initial-boundary value problem of a semilinear wave equation. This equation admits space-time dependent coefficients and a memory boundarylike antiperiodic condition. For regularity or existence of a unique strong solution, the...
- Existence and Decay Estimate of Global Solutions to Systems of Nonlinear Wave Equations with Damping and Source Terms. Yaojun Ye // Abstract & Applied Analysis;2013, p1
The initial-boundary value problem for a class of nonlinear wave equations system in bounded domain is studied. The existence of global solutions for this problem is proved by constructing a stable set and obtain the asymptotic stability of global solutions through the use of a difference...
- Global Existence and Blow-up of Weak Solutions for Nonlinear Wave Equations. Yunzhu Gao; Wei Guo; Tian Luan // Applied Mechanics & Materials;2014, Issue 630-642, p1565
In this paper, we discuss the nonlinear wave equations with nonlinear damping and source terms. By using the potential well methods, we get a result for the global existence and blow-up of the solutions.
- Asymptotic Behavior of Global Solutions for Some Nonlinear Wave Equation. Yongxian YAN // Applied Mechanics & Materials;2014, Issue 638-640, p1691
In this paper we study the asymptotic behavior of the global solutions to the initial-boundary value problem of the nonlinear wave equation with damping term by applying a difference inequality.