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1.
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   

2.
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   

3.
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   

4.
In this paper, we study the Cauchy problem of semilinear heat equations. By introducing a family of potential wells, we first prove the invariance of some sets and isolating solutions. Then we obtain a threshold result for the global existence and nonexistence of solutions. Finally we discuss the asymptotic behavior of the solution.  相似文献   

5.
We present a wave packet analysis of a class of possibly degenerate parabolic equations with variable coefficients. As a consequence, we prove local wellposedness of the corresponding Cauchy problem in spaces of low regularity, namely the modulation spaces, assuming a nonlinearity of analytic type. As another application, we deduce that the corresponding phase space flow decreases the global wave front set. We also consider the action on spaces of analytic functions, provided the coefficients are analytic themselves.  相似文献   

6.
In this paper the nonnegative classical solutions of a parabolic system with nonlinear boundary conditions are discussed. The existence and uniqueness of a nonnegative classical solution are proved. And some sufficient conditions to ensure the global existence and nonexistence of nonnegative classical solution to this problem are given.  相似文献   

7.
We prove the existence of solutions for a nonlocal equation arising from the mathematical modeling of MicroElectroMechanicalSystems (MEMS). The existence result, obtained within a suitable Implicit Function Theorem framework, is established under rather general boundary conditions and for bounded domains whose diameter is fairly small.  相似文献   

8.
9.
We consider the micropolar fluid system in a bounded domain of
and prove the existence and the uniqueness of a global strong solution with initial data being a perturbation of the stationary solution, whose existence is also obtained. We prove that these solutions converge uniformly to the stationary solutions with exponential decay rate. The technique of our analysis is the semigroups approach in L p -spaces. M. A. Rodríguez-Bellido is partially supported by D.G.E.S. and M.C. y T. (Spain), Projet BFM2003-06446-C02-01 and by M.E.C. (Spain), Projet MTM2006-07932.  相似文献   

10.
We study the global existence of solutions to a parabolic-parabolic system for chemotaxis with a logistic source in a two-dimensional domain, where the degradation order of the logistic source is weaker than quadratic. We introduce nonlinear production of a chemoattractant, and show the global existence of solutions under certain relations between the degradation and production orders.  相似文献   

11.
Maxwell-Bloch equations describe the propagation of an electromagnetic wave through a quantum medium. For any number of quantum levels, in space dimension 3, we show the global existence of weak (L2) solutions to the initial-value problem. In the case of smoother electromagnetic fields (with curl in L2), the solution is unique. For smooth data (Hs, s?2), the solutions remain smooth for all times.  相似文献   

12.
We consider two-dimensional mixed problems in an exterior domain for a semilinear strongly damped wave equation with a power-type nonlinearity |u|p|u|p. If the initial data have a small weighted energy, we shall derive a global existence and energy decay results in the case when the power pp of the nonlinear term satisfies p>6p>6.  相似文献   

13.
14.
Let (n?3) be a ball, and let fC3. We are concerned with the Neumann problem
  相似文献   

15.
In this paper, the existence and exponential stability of mild solutions of semilinear differential equations with random impulses are studied under non-uniqueness in a real separable Hilbert space. The results are obtained by using the Leray-Schauder alternative fixed point theorem.  相似文献   

16.
This paper is concerned with global existence and blow-up phenomena for an integrable two-component Camassa-Holm shallow water system. A new global existence result and several new blow-up results of strong solutions to the system are presented. Our obtained results for the system are sharp and improve considerably earlier results.  相似文献   

17.
Let
((1))
be a semilinear hyperbolic system, whereA is a real diagonal matrix and a mappingyF(x, t, y) is in with uniform bounds for (x, t) K 2.Oberguggenberger [6] has constructed a generalized solution to (1) whenA is an arbitrary generalized function andF has a bounded gradient with respect toy for (x, t) K 2. The above system, in the case when the gradient of the nonlinear termF with respect toy is not bounded, is the subject of this paper. F is substituted byF h() which has a bounded gradient with respect toy for every fixed (, ) and converges pointwise toF as 0. A generalized solution to
((2))
is obtained. It is compared to a continuous solution to (1) (if it exists) and the coherence between them is proved.  相似文献   

18.
In this paper we study a multiplicity result for a strongly indefinite semilinear elliptic system
  相似文献   

19.
We prove the global existence of the so-called H2 solutions for a nonlinear wave equation with a nonlinear dissipative term and a derivative type nonlinear perturbation. To show the boundedness of the second order derivatives we need a precise energy decay estimate and for this we employ a ‘loan’ method.  相似文献   

20.
It is well known that the solution of the classical linear wave equation with an initial condition with compact support and vanishing initial velocity also has a compact support included in a set depending on time: the support of the solution at time tt is causally related to that of the initial condition. Reed and Simon have shown that for a real-valued Klein–Gordon equation with (nonlinear) right-hand side −λu3λu3 (λ>0λ>0), causality still holds. We show the same property for a one-dimensional Klein–Gordon problem but with transmission and with a more general repulsive nonlinear right-hand side F(u)F(u). We also prove the global existence of a solution using the repulsiveness of FF. In the particular case F(u)=−λu3F(u)=λu3, the problem is a relativistic model for a quantum particle with repulsive self-interaction and tunnel effect at a semi-infinite potential step.  相似文献   

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