共查询到20条相似文献,搜索用时 15 毫秒
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M. O. Korpusov 《Theoretical and Mathematical Physics》2013,174(3):307-314
We consider the phenomenon of solution blowup for the system of equations describing surface water waves and also for the acoustic wave equation in viscous medium using the test-function method developed by Galactionov, Pokhozhaev, and Mitidieri. 相似文献
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This paper deals with degenerate diffusion equations with nonlocal sources. The local existence of a classical solution is given. By making use of super- and sub-solution method we show that the solution exists globally or blows up in finite time under some conditions. Furthermore, the blowup rates of the blowup solution are derived. 相似文献
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汪瑶瑶 《纯粹数学与应用数学》2017,33(1)
研究双曲平均曲率流中一类几何流方程周期解的爆破问题.引入合适的黎曼不变量,将该方程化为对角型的一阶拟线性双曲型方程组.该方程组在Lax意义下不是真正非线性的.假设初值是周期的,且在一个周期内全变差很小,此外假设初值还满足一定的结构条件,可以证得该几何流方程的周期解必在有限时间内发生爆破,解的生命跨度估计可以给出. 相似文献
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Blow-up theorems for nonlinear wave equations 总被引:14,自引:0,他引:14
Professor Robert T. Glassey 《Mathematische Zeitschrift》1973,132(3):183-203
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P. A. Chubenko 《Computational Mathematics and Mathematical Physics》2009,49(4):638-646
An initial-boundary value problem is considered for a fifth-order nonlinear equation describing the dynamics of a Kelvin-Voigt fluid with allowance for strong spatial dispersion in the presence of sources with a cubic nonlinearity. A local existence theorem is proved. The method of energy inequalities is used to find sufficient conditions for the solution to blowup in a finite time. 相似文献
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In this paper,we consider the following nonlinear wave equations:(■~2φ)/(■t~2)-(■~2φ)/(■x~2)+μ~2φ+v~2x~2φ+f(|φ|~2)φ=0,(■~2x)/(■t~2-(■~2X)/(■X~2)+α~2x+α~2x+v~2x|φ|~2+g(X)=0with the periodic-initial conditions:φ(x-π,t)=φ(x+π,t),x(x-π,t)=x(x+v,t),φ(x,0)=■_0(x),φ_t(x,0)=■_1(x),X(x,0)=■_0(x),x_t(x,0)=■_1(x),-∞相似文献
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Laila Girgis 《Applied mathematics and computation》2010,216(7):2226-7047
This paper studies the soliton perturbation that are described by three nonlinear wave equations. The adiabatic dynamics of the soliton parameters and the soliton velocity is obtained, in the presence of perturbation terms. The fixed point is also determined in a couple of cases. 相似文献
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Mitsuhiro Nakao 《Journal of Differential Equations》2006,227(1):204-229
We show the existence, size and some absorbing properties of global attractors of the nonlinear wave equations with nonlinear dissipations like ρ(x,ut)=a(x)r|ut|ut. 相似文献
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Finite-time blow-up for solutions of nonlinear wave equations 总被引:8,自引:0,他引:8
Robert T. Glassey 《Mathematische Zeitschrift》1981,177(3):323-340
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In this paper, five block preconditioning strategies are proposed to solve a class of nonlinear viscous wave equations. Implicit time-integration techniques from low order to high order are considered exclusively including implicit Euler (IE1) method, backward differentiation formulas (BDF2, BDF3) as well as the Crank–Nicholson (CN2) scheme. The CN2 method demonstrates superior performance compared to the BDF2 scheme for the problems considered in this work. In addition, the third-order accurate BDF3 scheme is found to be the most efficient in terms of computational cost for a prescribed accuracy level. Moreover, the benefit of this scheme increases for tighter error tolerances. 相似文献
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Paul Massatt 《Journal of Differential Equations》1983,48(3):334-349
In this paper we investigate both the existence and the limiting behavior for the equation , where A is a sectorial operator, ? is periodic in t, and ? satisfies certain regularity and growth assumptions. In most results on limiting behavior we will assume A has compact resolvent. We consider the equation as an abstract ODE defined on a paired space Xβ × Xα, 0 ? σ ? β < 1. With regard to the limiting behavior, one of our principal results will be to show that if there is a bounded set in one of the spaces considered, for which all points or trajectories enter into and remain, then there is a set J consisting of very “smooth” functions defined on all of the spaces considered, which is the maximum compact invariant set, uniformly asymptotically stable, connected, and having very strong attractivity properties in all these spaces. We will often show it attracts all points in a bounded set uniformly. We will give a few sharper results for the case where A = ?Δ. The work is motivated by recent papers of Webb and Fitzgibbon, and applies techniques found in recent papers by the author. 相似文献
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Yujin Liu 《印度理论与应用数学杂志》2012,43(3):279-300
This paper is concerned with the interactions of the elementary waves for the nonlinear degenerate wave equations. By analyzing the expressions of the elementary waves and the relative locations of the left state U l and the right state U r in the phase plane (u, v) we deal with the interactions of the elementary waves, especially the overtaking of shock wave and rarefaction wave from the same family. 相似文献