Global existence and nonexistence for nonlinear wave equations with damping and source terms
نویسندگان
چکیده
منابع مشابه
Global 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...
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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...
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In this article we focus on the global well-posedness of the differential equation utt − ∆u+ |u|k∂j(ut) = |u|p−1u in Ω× (0, T ), where ∂j is a sub-differential of a continuous convex function j. Under some conditions on j and the parameters in the equations, we obtain several results on the existence of global solutions, uniqueness, nonexistence and propagation of regularity. Under nominal assu...
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در این رساله به بررسی رفتار جواب های رده ای از معادلات دیفرانسیل با مشتقات جزیی در دامنه های کراندار می پردازیم . این معادلات به فرم نیم-خطی و غیر خطی برای مسایل مستقیم و معکوس مورد مطالعه قرار می گیرند . به ویژه، تاثیر شرایط مختلف فیزیکی را در مساله، نظیر وجود موانع و منابع، پراکندگی و چسبندگی در معادلات موج و گرما بررسی می کنیم و به دنبال شرایطی می گردیم که متضمن وجود سراسری یا عدم وجود سراسر...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2002
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-02-03034-9