共查询到20条相似文献,搜索用时 0 毫秒
1.
Caisheng Chen 《Journal of Evolution Equations》2006,6(1):29-43
In this paper, we study the global existence, L∞ estimates and decay estimates of solutions for the quasilinear parabolic system ut = div (|∇ u|m ∇ u) + f(u, v), vt = div (|∇ v|m ∇ v) + g(u,v) with zero Dirichlet boundary condition in a bounded domain Ω ⊂ RN. In particular, we find a critical value for the existence and nonexistence of global solutions to the equation ut = div (|∇ u|m ∇ u) + λ |u|α - 1 u. 相似文献
2.
Zhong Tan Rongcong Guo 《NoDEA : Nonlinear Differential Equations and Applications》2011,18(4):459-481
In this paper, we construct the global weak solutions to the initial-boundary problem for the Navier–Stokes system with capillarity
in the half space
\mathbbR+1{\mathbb{R}_+^1}. The result extends Eugene Tsyganov’s existence theorem which considered the problem in the finite region published in J.
Differential Equaions 245:3936–3955, 2008. 相似文献
3.
Min-Chun Hong 《Calculus of Variations and Partial Differential Equations》2011,40(1-2):15-36
In the 1960s, Ericksen and Leslie established the hydrodynamic theory for modelling liquid crystal flow. In this paper, we investigate a simplified model of the Ericksen?CLeslie system, which is a system of the Navier?CStokes equations coupled with the harmonic map flow. We prove global existence of solutions to the Ericksen?CLeslie system in ${\mathbb{R}^{2}}$ with initial data, where the solutions are regular except for at a finite number of singular times. 相似文献
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This paper deals with the quasilinear degenerate Keller–Segel system (KS) of parabolic–parabolic type. The global existence of weak solutions to (KS) is established when (m denotes the intensity of diffusion and q denotes the nonlinearity) without restriction on the size of initial data; note that corresponds to generalized Fujita?s exponent. The result improves both Sugiyama (2007) [14, Theorem 1] and Sugiyama and Kunii (2006) [15, Theorem 1] in which it is assumed that . 相似文献
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7.
Kazuki Aoki Nakao Hayashi Pavel I. Naumkin 《NoDEA : Nonlinear Differential Equations and Applications》2016,23(6):65
We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation where \(n=1,2\). We prove global existence of small solutions under the growth condition of \(f\left( u\right) \) satisfying \(\left| \partial _{u}^{j}f\left( u\right) \right| \le C\left| u\right| ^{p-j},\) where \(p>1+\frac{4}{n},0\le j\le 3\).
相似文献
8.
Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries 总被引:2,自引:0,他引:2
Ling-hua KONG~ 《中国科学A辑(英文版)》2007,50(9):1251-1266
This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries.By using super-and sub-solution techniques,we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively,and then give the necessary and sufficient conditions that two components u and v blow up simultaneously.Finally,the uniform blow-up profiles in the interior are presented. 相似文献
9.
Hongyan Ma 《Applicable analysis》2018,97(10):1814-1827
In this paper, we investigate the global well-posedness for the 3D Newton-Boussinesq equations in a large class of non-decaying vorticity. With the help of the Fourier analysis and the coupling structure, we establish the global-in-time estimate of vorticity in non-Lipschitz vector field. This estimate together with a new observation enables us to obtain the global existence of non-decaying vorticity. More importantly, we show this solution is unique as time develops. 相似文献
10.
This paper is devoted to the analysis of nonnegative solutions for a degenerate parabolic–elliptic Patlak–Keller–Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to prove the existence of a global weak solution under a smallness condition on the mass of the initial data, thereby completing previous results on finite blow-up for large masses. Under some higher regularity condition on solutions, the uniqueness of solutions is proved by using a classical duality technique. 相似文献
11.
This paper discusses the weakly coupled nonlinear Schrödinger equations in the supercritical case. With the best constant of the Gagliardo-Nirenberg inequality, we derive a sufficient condition for the global existence of solutions; this condition is expressed in terms of stationary solutions (nonlinear ground state). 相似文献
12.
Franç Bouchut 《偏微分方程通讯》2013,38(8-9):1337-1365
We are studying the existence and weak stability of a Vlasov–Poisson syste with two typs of particles , in which the electrons are supposed to be at thermal equilibrium. This modifies the source term in the Poisson equaitonm\, and estimates in the Marcinkiewicz space M3 for the potential are used to get the strong compactness of approximations using a new regularized kernal which preservs an approriate energy inequality. 相似文献
13.
Recently, Fan, Gao and Liu proposed a kind of rotation-two-component Camassa–Holm system. In this paper, we investigate whether the rotation-two-component Camassa–Holm system admits peakon-delta weak solutions in distribution sense. As special reductions, all peakon solutions for generalized Dullin–Gottwald–Holm system, two-component Camassa–Holm system, Dullin–Gottwald–Holm equation and Camassa–Holm equation are recovered from the corresponding results of rotation-two-component Camassa–Holm system. 相似文献
14.
Masaki Kurokiba Takayoshi Ogawa Futoshi Takahashi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(5):840-867
We show the global existence of small solution to the perturbed Keller–Segel system of simplified version. Our system has
a perturbed nonlinear term of worse sign, therefore the existence and uniqueness of solution is not really obvious. The local
existence theorem is obtained by a variational observation for the elliptic part.
相似文献
15.
Chenglin Li 《Journal of Applied Mathematics and Computing》2018,57(1-2):105-119
This paper is concerned with a cross-diffusion predator–prey system with a free boundary over a one-dimensional habitat. The free boundary shows the spreading front of the prey and predator which implies that the velocity of the expanding front is proportional to the gradients of the prey and predator. By the contraction mapping principle, \(L^{p}\) estimates and Schauder estimates of parabolic equations, the local and global existence and uniqueness of classical solutions are established for this system. 相似文献
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This paper studies the solutions of a reaction–diffusion system with nonlinearities that generalize the Lengyel–Epstein and FitzHugh–Nagumo nonlinearities. Sufficient conditions are derived for the global asymptotic stability of the solutions. Furthermore, we present some numerical examples. 相似文献
18.
We study the existence theory for the Cucker–Smale–Navier–Stokes (in short, CS–NS) equations in two dimensions. The CS–NS equations consist of Cucker–Smale flocking particles described by a Vlasov-type equation and incompressible Navier–Stokes equations. The interaction between the particles and fluid is governed by a drag force. In this study, we show the global existence of weak solutions for this system. We also prove the global existence and uniqueness of strong solutions. In contrast with the results of Bae et al. (2014) on the CS–NS equations considered in three dimensions, we do not require any smallness assumption on the initial data. 相似文献
19.
Xianwen Zhang 《Applied Mathematics Letters》2013,26(11):1087-1093
We prove the existence of a global nonnegative weak solution to the Cauchy problem of the Vlasov–Poisson–BGK system for initial datum having finite mass and energy and belonging to with . 相似文献
20.
Cleopatra Christoforou 《Journal of Differential Equations》2012,252(3):2845-2863
The isometric immersion problem for surfaces embedded into is studied via the fluid dynamic framework introduced in Chen et al. (2010) [6] as a system of balance laws of mixed-type. The techniques developed in the theory of weak solutions of bounded variation in continuum physics are employed to deal with the isometric immersions in the setting of differential geometry. The so-called BV framework is formed that establishes convergence of approximate solutions of bounded variation to the Gauss–Codazzi system and yields the isometric realization of two-dimensional surfaces into . Local and global existence results are established for weak solutions of small bounded variation to the Gauss–Codazzi system for negatively curved surfaces that admit equilibrium configurations. As an application, the case of catenoidal shell of revolution is provided. 相似文献