共查询到20条相似文献,搜索用时 0 毫秒
1.
Yue Liu 《Mathematische Annalen》2006,335(3):717-735
Considered herein are the problems of the existence of global solutions and the formation of singularities for a new nonlinear
shallow water wave equation derived by Dullin, Gottward and Holm. Blow-up can occur only in the form of wave-breaking. A wave-breaking
mechanism for solutions with certain initial profiles is described in detail and the exact blow-up rate is established. The
blow-up set for a class of initial profiles and lower bounds of the existence time of the solution are also determined. 相似文献
2.
3.
Fucai Li 《Applied Mathematics Letters》2004,17(12):686
This paper deals with the higher-order Kirchhoff-type equation with nonlinear dissipationutt+(∫Ω׀Dmu׀2dx)q(−Δ)mu+ut׀ut׀r=׀u׀pu,xΩ,t>0,in a bounded domain, where m < 1 is a positive integer, q, p, r < 0 arepositive constants. We obtain that the solution exists globally if p ≤ r, while ifp > max r, 2q , then for any initial data with negative initial energy, the solution blowsup at finite time in Lp+2 norm. 相似文献
4.
主要研究在Dirichlet边界条件或Neumann边界条件下的一类非局部非线性的扩散方程问题.在适当的假设下,证明解的存在性、唯一性、比较原则、以及解对初边值条件的连续依赖性,并就给定的初边值条件,证明解在有限时刻全局爆破. 相似文献
5.
Multiple blow-up for a porous medium equation with reaction 总被引:1,自引:0,他引:1
The present paper is concerned with the Cauchy problem
$\left\{{ll}\partial_t u = \Delta u^m + u^p & \quad {\rm in}\; \mathbb R^N \times (0,\infty),\\ u(x,0) = u_0(x) \geq 0 & \quad {\rm in}\; \mathbb R^N, \right.$\left\{\begin{array}{ll}\partial_t u = \Delta u^m + u^p & \quad {\rm in}\; \mathbb R^N \times (0,\infty),\\ u(x,0) = u_0(x) \geq 0 & \quad {\rm in}\; \mathbb R^N, \end{array}\right. 相似文献
6.
Amin Esfahani Luiz Gustavo Farah Hongwei Wang 《Nonlinear Analysis: Theory, Methods & Applications》2012
In this paper we prove local well-posedness in L2(R) and H1(R) for the generalized sixth-order Boussinesq equation utt=uxx+βuxxxx+uxxxxxx+(|u|αu)xx. Our proof relies in the oscillatory integrals estimates introduced by Kenig et al. (1991) [14]. We also show that, under suitable conditions, a global solution for the initial value problem exists. In addition, we derive the sufficient conditions for the blow-up of the solution to the problem. 相似文献
7.
Shuyin Wu 《Journal of Differential Equations》2009,246(11):4309-4321
This paper is concerned with global existence and blow-up phenomena for the weakly dissipative Camassa-Holm equation. A new global existence result and a new blow-up result for strong solutions to the equation with certain profiles are presented. The obtained results improve considerable the previous results. 相似文献
8.
In this paper, we consider the global existence and blow-up for the weakly dissipative Novikov equation. We firstly establish the local well-posedness for the weakly dissipative Novikov equation by Kato’s theorem. Then we present some blow-up results. Finally, we present the global existence of strong solutions to the weakly dissipative equation. 相似文献
9.
In this paper, we consider initial boundary value problem of the generalized Boussinesq equation with nonlinear interior source and boundary absorptive terms. We establish firstly the local existence of solutions by standard Galerkin method. Then we prove both the global existence of the solution and a general decay of the energy functions under some restrictions on the initial data. We also prove a blow-up result for solutions with positive and negative initial energy respectively. 相似文献
10.
Changfeng Gui 《纯数学与应用数学通讯》1995,48(5):471-500
We study the blow-up set of a porous medium type equation with source. Under some technical conditions, we prove that if the blow-up set is a bounded smooth region, then it must be a ball with a certain radius. This problem can be reduced to a sublinear elliptic equation coupled with an overdetermined boundary condition. Roughly speaking, the overdetermined boundary condition forces the domain to be a ball. Because the nonlinear term is sublinear and then non-Lipschitz, many difficulties arise if one wants to use the moving plane method to reach the goal. In particular, the Hopf boundary lemma is not applicable to this problem. Instead, we investigate various related problems in a half space and a problem in the first quadrant of the entire space, and then use the symmetry results obtained for these problems to overcome the obstacles encountered. ©1995 John Wiley & Sons, Inc. 相似文献
11.
This paper deals with the blow-up properties of positive solutions to a nonlinear parabolic equation with a localized reaction source and a nonlocal boundary condition. Under certain conditions, the blowup criteria is established. Furthermore, when f(u)=up, 0<p?1, the global blowup behavior is shown, and the blowup rate estimates are also obtained. 相似文献
12.
In this article, a porous medium equation with nonlocal boundary condition and a localized source is studied. The results of the existence of global solutions or blow-up of solutions are given. The blow-up rate estimates are also obtained under some conditions. 相似文献
13.
Yohei Fujishima 《Journal of Differential Equations》2018,264(11):6809-6842
We are concerned with the existence of global in time solution for a semilinear heat equation with exponential nonlinearity
(P) where is a continuous initial function. In this paper, we consider the case where decays to ?∞ at space infinity, and study the optimal decay bound classifying the existence of global in time solutions and blowing up solutions for (P). In particular, we point out that the optimal decay bound for is related to the decay rate of forward self-similar solutions of . 相似文献
14.
This paper concerns the study of the numerical approximation for the following initialboundary value problem
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