共查询到20条相似文献,搜索用时 15 毫秒
1.
Lamia Mâatoug 《Journal of Functional Analysis》2006,233(2):583-618
We study the existence and the asymptotic behavior of positive solutions for the parabolic equation on D×(0,∞), where is a some unbounded domain in and V belongs to a new parabolic class J∞ of singular potentials generalizing the well-known parabolic Kato class at infinity P∞ introduced recently by Zhang. We also show that the choice of this class is essentially optimal. 相似文献
2.
In this paper we investigate the global existence and energy decay rate for the solution of a coupled hyperbolic system. The semi-explicit energy decay rate is established by using piecewise multiplier techniques and weighted integral inequality. We extend the energy decay result in Alabau-Boussouira [F. Alabau-Boussouira, Convexity and weighted integral inequalities for energy decay rates of nonlinear dissipative hyperbolic systems, Appl. Math. Optim. 51 (2005) 61-105] for a single equation to the coupled hyperbolic system. 相似文献
3.
We consider an equation modeling the evolution of a viscous liquid thin film wetting a horizontal solid substrate destabilized by an electric field normal to the substrate. The effects of the electric field are modeled by a lower order non-local term. We introduce the good functional analysis framework to study this equation on a bounded domain and prove the existence of weak solutions defined globally in time for general initial data (with finite energy). 相似文献
4.
Akbar B. Aliev Anar A. Kazimov 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(1):91-102
We consider the Cauchy problem for systems of semilinear hyperbolic equations. Using the Lp→Lq type estimation for the corresponding linear parts, the existence and uniqueness of weak global solutions are investigated. We also established the behavior of solutions and their derivatives as t→+∞. Using the method of test functions developed in the works (Mitidieri and Pokhozhaev, 2001 [11], Veron and Pohozaev, 2001 [12] and Caristi, 2000 [23]) we obtain the analogue of the Fujita-Hayakawa type criterion for the absence of global solutions to some system of semilinear hyperbolic inequalities with damping. It follows that the conditions of existence theorem imposed on the growth of nonlinear parts are exact in some sense. 相似文献
5.
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
6.
In this paper a class of semilinear thermoelastic contact problems is considered and the existence and exponential decay of the weak solutions are obtained. 相似文献
7.
In this paper we consider a semilinear Petrovsky equation with damping and source terms. It is proved that the solution blows up in finite time if the positive initial energy satisfies a suitable condition. Moreover for the linear damping case, we show that the solution blows up in finite time even for vanishing initial energy. This is an important breakthrough, since it is only well known that the solution blows up in finite time if the initial energy is negative from all the previous literature. 相似文献
8.
9.
Wenjun Liu 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(1):244-1904
This paper studies the Cauchy problem for the coupled system of nonlinear Klein-Gordon equations with damping terms. We first state the existence of standing wave with ground state, based on which we prove a sharp criteria for global existence and blow-up of solutions when E(0)<d. We then introduce a family of potential wells and discuss the invariant sets and vacuum isolating behavior of solutions for 0<E(0)<d and E(0)≤0, respectively. Furthermore, we prove the global existence and asymptotic behavior of solutions for the case of potential well family with 0<E(0)<d. Finally, a blow-up result for solutions with arbitrarily positive initial energy is obtained. 相似文献
10.
In this paper we consider the Cauchy problem of semilinear parabolic equations with nonlinear gradient terms a(x)|u|q−1u|∇u|p. We prove the existence of global solutions and self-similar solutions for small initial data. Moreover, for a class of initial data we show that the global solutions behave asymptotically like self-similar solutions as t→∞. 相似文献
11.
In this paper, we prove the existence and the uniqueness of global solution for the Cauchy problem for the generalized Boussinesq equation. Under some assumptions, we also show that the L∞ norm of small solution of the Cauchy problem for the generalized Boussinesq equation decays to zero as t tends to the infinity. 相似文献
12.
Thierry Cazenave Flávio Dickstein Fred B. Weissler 《Journal of Differential Equations》2009,246(7):2669-568
In this paper, given 0<α<2/N, we prove the existence of a function ψ with the following properties. The solution of the equation ut−Δu=α|u|u on RN with the initial condition u(0)=ψ is global. On the other hand, the solution with the initial condition u(0)=λψ blows up in finite time if λ>0 is either sufficiently small or sufficiently large. 相似文献
13.
We consider a system coupling the incompressible Navier-Stokes equations to the Vlasov-Fokker-Planck equation. The coupling arises from a drag force exerted by each other. We establish existence of global weak solutions for the system in two and three dimensions. Furthermore, we obtain the existence and uniqueness result of global smooth solutions for dimension two. In case of three dimensions, we also prove that strong solutions exist globally in time for the Vlasov-Stokes system. 相似文献
14.
Noriko Mizoguchi 《Journal of Differential Equations》2004,205(2):298-328
This paper is concerned with blowup phenomena of solutions for the Cauchy and the Cauchy-Dirichlet problem of
(P) 相似文献
15.
Yang Cao 《Journal of Differential Equations》2009,246(12):4568-4590
This paper concerns with the Cauchy problems of semilinear pseudo-parabolic equations. After establishing the necessary existence, uniqueness and comparison principle for mild solutions, which are also classical ones provided that the initial data are appropriately smooth, we investigate large time behavior of solutions. It is shown that there still exist the critical global existence exponent and the critical Fujita exponent for pseudo-parabolic equations and that these two critical exponents are consistent with the corresponding semilinear heat equations. 相似文献
16.
Yasuhito Miyamoto 《Journal of Differential Equations》2010,249(8):1853-1870
Let (n?3) be a ball, and let f∈C3. We are concerned with the Neumann problem
17.
Goro Akagi 《Journal of Differential Equations》2011,250(4):1850-1812
This paper addresses the analysis of dynamical systems generated by doubly nonlinear evolution equations governed by subdifferential operators with non-monotone perturbations in a reflexive Banach space setting. In order to construct global attractors, an approach based on the notion of generalized semiflow is employed instead of the usual semigroup approach, since solutions of the Cauchy problem for the equation might not be unique. Moreover, the preceding abstract theory is applied to a generalized Allen-Cahn equation as well as a semilinear parabolic equation with a nonlinear term involving gradients. 相似文献
18.
The Cauchy problem for a class of semilinear pseudo-hyperbolic equations is considered. For the corresponding linear problems, we obtain L p → L q estimates. By using these estimates, we prove global solvability theorems. We also establish the behavior of solutions as t → + ∞. 相似文献
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20.
Ross G. Pinsky 《Journal of Differential Equations》2006,220(2):407-433
Consider classical solutions u∈C2(Rn×(0,∞))∩C(Rn×[0,∞)) to the parabolic reaction diffusion equation