Metastable Energy Strata in Weakly Nonlinear Wave Equations
نویسندگان
چکیده
منابع مشابه
On the Boltzmann Equation for Weakly Nonlinear Wave Equations
We explain how the kinetic theory of L. Boltzmann is applied to weakly nonlinear wave equations.
متن کاملWave group dynamics in weakly nonlinear long-wave models
Wave group dynamics is studied in the framework of the extended Korteweg-de Vries equation. The nonlinear Schrodinger equation is derived for weakly nonlinear wave packets, and the condition for modulational instability is obtained. It is shown that wave packets are unstable only for a positive sign of the coe cient of the cubic nonlinear term in the extended Korteweg-de Vries equation, and for...
متن کاملFinite Energy Travelling Waves for Nonlinear Damped Wave Equations
E(u,ut) = f |Vu|2 + m\u\2 + |ut|2 dx — [ |u|"+1 dx, (1.3) 2 JRn a+ 1 JR„ which represents a Lyapunov function of the problem, i.e., it is decreasing along any nonstationary trajectory of (1.1). Employing the potential-well arguments of PAYNE-SATTINGER [16] one observes that any solution of (1.1) emanating from sufficiently small initial data exists globally for all t e R+ and tends to zero with...
متن کاملNonlinear Wave Equations
where := −∂2 t +∆ and u[0] := (u, ut)|t=0. The equation is semi-linear if F is a function only of u, (i.e. F = F (u)), and quasi-linear if F is also a function of the derivatives of u (i.e. F = F (u,Du), where D := (∂t,∇)). The goal is to use energy methods to prove local well-posedness for quasilinear equations with data (f, g) ∈ Hs × Hs−1 for large enough s, and then to derive Strichartz esti...
متن کاملNonlinear Wave Equations
This paper explores the properties of nonlinear wave equations. The proof for the existence and uniqueness of solutions to the 1+1 dimensional linear wave equation with smooth data is given. The D’Alembert formula is then presented in its full generality for the nonlinear equation. Important properties like the domain of dependence and propagation of information are discussed and motivated. The...
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: Communications in Partial Differential Equations
سال: 2012
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605302.2012.683503