共查询到20条相似文献,搜索用时 15 毫秒
1.
We show that the supremum norm of solutions with small initial data of the generalized Benjamin-Bona-Mahony equation ut-△ut=(b,▽u)+up(a,▽u)in x?Rn,n≥2, with integer p≥3 , decays to zero like t-2/3 if n=2 and like t-1+6, for any δ0, if n≥3, when t tends to infinity. The proofs of these results are based on an analysis of the linear equation ut-△=(b,▽u)) and the associated oscillatory integral which may have nonisolated stationary points of the phase function. 相似文献
2.
Tokio Matsuyama 《Journal of Mathematical Analysis and Applications》2002,271(2):467-492
We consider the initial-boundary value problem for the wave equation with a dissipation a(t,x)ut in an exterior domain, whose boundary meets no geometrical condition. We assume that the dissipation a(t,x)ut is effective around the boundary and a(t,x) decays as |x|→∞. We shall prove that the total energy does not in general decay, and the solution is asymptotically free as the time goes to infinity. Further, we shall show that the local energy decays like O(t−1) (t→∞). 相似文献
3.
Kosuke Ono 《Journal of Mathematical Analysis and Applications》2003,286(2):540-562
Consider the initial boundary value problem for the linear dissipative wave equation (□+∂t)u=0 in an exterior domain . Using the so-called cut-off method together with local energy decay and L2 decays in the whole space, we study decay estimates of the solutions. In particular, when N?3, we derive Lp decays with p?1 of the solutions. Next, as an application of the decay estimates for the linear equation, we consider the global solvability problem for the semilinear dissipative wave equations (□+∂t)u=f(u) with f(u)=|u|α+1,|u|αu in an exterior domain. 相似文献
4.
We consider the nonlinear Schrödinger equation (NLSH) with the convolution combined term (CNLSH) (CNLSH) in the energy space . We firstly use a variational approach to give a dichotomy of scattering and blow up for the radial solution with the energy below the threshold, which is given by the ground state W for the energy‐critical NLS: iut+Δu=?|u|4u. The basic strategy is the concentration‐compactness arguments from Kenig and Merle. We overcome the main difficulties coming from the lack of scaling invariance and the non‐local property of the convolution term. Our result shows that the focusing, ‐critical term ?|u|4u plays the decisive role of the threshold of the scattering solution of (CNLSH) in the energy space. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
5.
In this paper, we investigate the large‐time decay and stability to any given global smooth solutions of the 3‐D incompressible inhomogeneous Navier‐Stokes equations. In particular, we prove that given any global smooth solution (a,u) of (1.2), the velocity field u decays to 0 with an explicit rate, which coincides with the L2 norm decay for the weak solutions of the 3‐D classical Navier‐Stokes system [26,29] as t goes to ∞. Moreover, a small perturbation to the initial data of (a,u) still generates a unique global smooth solution to (1.2), and this solution keeps close to the reference solution (a,u) for t > 0. We should point out that the main results in this paper work for large solutions of (1.2). © 2010 Wiley Periodicals, Inc. 相似文献
6.
Salim A. Messaoudi 《Mathematische Nachrichten》2001,231(1):105-111
In this paper we consider the nonlinearly damped semilinear wave equation utt – Δu + aut |ut|m – 2 = bu|u|p – 2 associated with initial and Dirichlet boundary conditions. We prove that any strong solution, with negative initial energy, blows up in finite time if p > m. This result improves an earlier one in [2]. 相似文献
7.
Vasilii V. Kurta 《Archiv der Mathematik》2006,87(4):368-374
We generalize and improve recent non-existence results for global solutions to the Cauchy problem for the inequality
as well as for the equation ut = Δu + |u|q in the half-space
.
Received: 16 September 2005 相似文献
8.
In this paper, we consider the global existence, uniqueness and L
∞ estimates of weak solutions to quasilinear parabolic equation of m-Laplacian type u
t
− div(|∇u|
m−2∇u) = u|u|
β−1 ∫Ω |u|
α
dx in Ω × (0,∞) with zero Dirichlet boundary condition in tdΩ. Further, we obtain the L
∞ estimate of the solution u(t) and ∇u(t) for t > 0 with the initial data u
0 ∈ L
q
(Ω) (q > 1), and the case α + β < m − 1. 相似文献
9.
Justin Holmer 《偏微分方程通讯》2013,38(5):878-905
We consider solutions u(t) to the 3d NLS equation i? t u + Δu + |u|2 u = 0 such that ‖xu(t)‖ L 2 = ∞ and u(t) is nonradial. Denoting by M[u] and E[u], the mass and energy, respectively, of a solution u, and by Q(x) the ground state solution to ?Q + ΔQ + |Q|2 Q = 0, we prove the following: if M[u]E[u] < M[Q]E[Q] and ‖u 0‖ L 2 ‖?u 0‖ L 2 > ‖Q‖ L 2 ‖?Q‖ L 2 , then either u(t) blows-up in finite positive time or u(t) exists globally for all positive time and there exists a sequence of times t n → + ∞ such that ‖?u(t n )‖ L 2 → ∞. Similar statements hold for negative time. 相似文献
10.
L. V. Davydova 《Journal of Mathematical Sciences》2005,129(1):3566-3572
Let L be a linear, uniformly elliptic, second-order operator of nondivergent type with measurable and bounded coefficients and α and K be constants, 0 < α < 1, K > 0. We study the growth rate of solutions of the quasilinear parabolic inequality Lu − u
t
≥ − (|∇ u|1+α + K at a boundary point.__________Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 10, Suzdal Conference-4, 2003. 相似文献
11.
Donglong Li Zhengde Dai Xuhong Liu 《Journal of Mathematical Analysis and Applications》2007,330(2):934-948
In this paper, the two-dimensional generalized complex Ginzburg–Landau equation (CGL)
ut=ρu−Δφ(u)−(1+iγ)Δu−νΔ2u−(1+iμ)|u|2σu+αλ1(|u|2u)+β(λ2)|u|2