Long time behavior of solutions of gKdV equations
نویسندگان
چکیده
منابع مشابه
Multi-soliton solutions for the supercritical gKdV equations
For the L subcritical and critical (gKdV) equations, Martel [11] proved the existence and uniqueness of multi-solitons. Recall that for any N given solitons, we call multi-soliton a solution of (gKdV) which behaves as the sum of these N solitons asymptotically as t → +∞. More recently, for the L supercritical case, Côte, Martel and Merle [4] proved the existence of at least one multi-soliton. I...
متن کاملBlow - up Solutions for Gkdv Equations with K Blow
In this paper we consider the slightly L-supercritical gKdV equations ∂tu + (uxx + u|u|)x = 0, with the nonlinearity 5 < p < 5 + ε and 0 < ε ≪ 1 . In the previous paper [10] we know that there exists an stable selfsimilar blow-up dynamics for slightly L-supercritical gKdV equations. Such solution can be viewed as solutions with single blow-up point. In this paper we will prove the existence of ...
متن کاملLong Time Behavior of Solutions to the 3d Compressible Euler Equations with Damping
The effect of damping on the large-time behavior of solutions to the Cauchy problem for the three-dimensional compressible Euler equations is studied. It is proved that damping prevents the development of singularities in small amplitude classical solutions, using an equivalent reformulation of the Cauchy problem to obtain effective energy estimates. The full solution relaxes in the maximum nor...
متن کاملLarge Time Behavior of Solutions to Some Degenerate Parabolic Equations
The purpose of this paper is to study the limit in L(Ω), as t→∞, of solutions of initial-boundary-value problems of the form ut−∆w = 0 and u ∈ β(w) in a bounded domain Ω with general boundary conditions ∂w ∂η + γ(w) 3 0. We prove that a solution stabilizes by converging as t → ∞ to a solution of the associated stationary problem. On the other hand, since in general these solutions are not uniqu...
متن کاملLong Time Behaviour of Solutions to Nonlinear Wave Equations
G(u,u',u") = 0, (1) where u = u(x, x,..., x), and u', u" denote all the first and second partial derivatives of u. For simplicity we will assume here that both u and G are scalars and denote by ua, uab, the partial derivatives dau and respectively dahu; a,b =1,2, ..., n+1. Let u (x) be a given solution of (1). Our equation is said to be elliptic or hyperbolic at u°(x) according to whether 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: Journal of Mathematical Analysis and Applications
سال: 2012
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2012.01.031