Global nonexistence of solutions for systems of quasilinear hyperbolic equations with damping and source terms
نویسندگان
چکیده
منابع مشابه
On the decay of solutions for a class of quasilinear hyperbolic equations with non-linear damping and source terms
In this paper, we consider the non-linear wave equation utt − ut − div(|∇u|∇u) + a|ut | ut = b|u|u a; b¿0, associated with initial and Dirichlet boundary conditions. Under suitable conditions on , m, and p, we give precise decay rates for the solution. In particular, we show that for m = 0, the decay is exponential. This work improves the result by Yang (Math. Meth. Appl. Sci. 2002; 25:795–814)...
متن کاملGlobal Nonexistence of Positive Initial-Energy Solutions for Coupled Nonlinear Wave Equations with Damping and Source Terms
and Applied Analysis 3 ordinary differential inequality, next given the sufficient conditions of blow-up of the solution of 1.4 by the inequality. In 21 , Hao et al. considered the single-wave equation of the form utt − div ( g ( |∇u| ) ∇u ) h ut f u , x ∈ Ω, t > 0 1.5 with initial and Dirichlet boundary condition, where g satisfies condition 1.2 and g s ≥ b1 b2s, q ≥ 0. 1.6 The damping term ha...
متن کاملGlobal Existence and Nonexistence for Nonlinear Wave Equations with Damping and Source Terms
We consider an initial-boundary value problem for a nonlinear wave equation in one space dimension. The nonlinearity features the damping term |u|m−1 ut and a source term of the form |u|p−1 u, with m, p > 1. We show that whenever m ≥ p, then local weak solutions are global. On the other hand, we prove that whenever p > m and the initial energy is negative, then local weak solutions cannot be gl...
متن کاملUniform stabilization of solutions to a quasilinear wave equation with damping and source terms
In this note we prove the exponential decay of solutions of a quasilinear wave equation with linear damping and source terms.
متن کاملOn the Global Solvability of Solutions to a Quasilinear Wave Equation with Localized Damping and Source Terms
where M(s) is a C1-class function on [0,+∞[ satisfying M(s) ≥m0 > 0, for s ≥ 0, with m0 constant, a is a smooth nonnegative function but vanishes somewhere in Ω, f (u) is a nonlinear term like f (u) ∼−|u|αu, and g is a real-valued function. The problem (1.1), when M(s) = 1 and f is some type of nonlinear function, has been studied by Zuazua [10] and Nakao [9]. Recently, Cabanillas et al. have t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Boundary Value Problems
سال: 2014
ISSN: 1687-2770
DOI: 10.1186/s13661-014-0251-y