共查询到20条相似文献,搜索用时 0 毫秒
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Pavol Quittner 《Mathematische Annalen》2001,320(2):299-305
We prove universal a priori estimates of global positive solutions of the parabolic problem in , on . Here is a bounded domain in , , and p < 5 if n=3.
Received April 6, 2000 / Accepted September 21, 2000 / Published online February 5, 2001 相似文献
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G. Wolansky 《Monatshefte für Mathematik》2001,132(3):255-261
We compare the solution of to the solution of the same equation where f is replaced by a “concentrated” source . As a result we derive some estimates on the solution in spatial norm, locally uniformly in t, with respect to the norm of for any integer . In the case we obtain a critical inequality relating the norm of to an exponential norm of u.
(Received 1 September 2000; in revised form 17 January 2001) 相似文献
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This paper is concerned with traveling waves of reaction-diffusion systems. The definition of coupled quasi-upper and quasi-lower solutions is introduced for systems with mixed quasimonotone functions, and the definition of ordered quasi-upper and quasi-lower solutions is also given for systems with quasimonotone nondecreasing functions. By the monotone iteration method, it is shown that if the system has a pair of coupled quasi-upper and quasi-lower solutions, then there exists at least a traveling wave solution. Moreover, if the system has a pair of ordered quasi-upper and quasi-lower solutions, then there exists at least a traveling wavefront. As an application we consider the delayed system of a mutualistic model. 相似文献
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Klaus Deckelnick 《manuscripta mathematica》1999,98(2):265-274
We study the regularity of certain weak solutions for the curve shortening flow in arbitrary codimension. These solutions
arise as limits of a regularization process which is related to an approach suggested by Calabi. We prove that the set of
times for which such a weak solution is not smooth has Hausdorff dimension at most ?.
Received: 23 May 1998 / Revised version: 7 September 1998 相似文献
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Mohammed GUEDDA Robert KERSNER 《NoDEA : Nonlinear Differential Equations and Applications》2003,10(1):1-13
Geometric properties of shape functions of self-similar solution to the equation are studied, and q are positive numbers. These shapes-the solutions of the corresponding nonlinear ODE-are of very different nature. The properties
usually depend on three critical values of q (1, 3/2 and 2). For the range 1<q<2 the dependence of is more remarkable, for example there is no global existence in general. 相似文献
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Noriko Mizoguchi 《Mathematische Zeitschrift》2002,239(2):215-229
This paper is concerned with a Cauchy problem
where and is a nonnegative radially symmetric function in with compact support. Denote the solution of (P) by . Let if and $p^{\ast} = 1+6/(N-10) N \geq 11 p_{\ast} < p < p^{\ast} \lambda_{\varphi} > 0 $ such that:
(i) If $ \lambda < \lambda_{\varphi} u_{\lambda} $ exists globally in time in the classical sense and converges to zero locally uniformly in as .
(ii) If , then $ u_{\lambda} $ blows upincompletely in finite time.
(iii) If , then blows upcompletely in finite time.
Received: 20 December 1999; in final form: 26 May 2000 / Published online: 4 May 2001 相似文献
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Boundary regularity for nonlinear elliptic systems 总被引:3,自引:0,他引:3
J.F. Grotowski 《Calculus of Variations and Partial Differential Equations》2002,15(3):353-388
We consider questions of boundary regularity for solutions of certain systems of second-order nonlinear elliptic equations.
We obtain a general criterion for a weak solution to be regular in the neighbourhood of a given boundary point. The proof
yields directly the optimal regularity for the solution in this neighbourhood. This result is new for the situation under
consideration (general nonlinear second order systems in divergence form, with inhomogeneity obeying the natural growth conditions).
Received: 6 July 2001 / Accepted: 27 September 2001 / Published online: 28 February 2002 相似文献
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Shuxia Pan Wan-Tong Li Guo Lin 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,20(3):377-392
This paper is concerned with the travelling wave fronts of nonlocal reaction-diffusion systems with delays. The existence
of travelling wave fronts for nonlocal reaction-diffusion systems with delays is established by using Schauder’s fixed point
theorem and upper-lower solution technique. Then these results are applied to the nonlocal delayed Logistic model and the
delayed Belousov-Zhabotinskii reaction-diffusion system. Our results show that the time delay can reduce the minimal wave
speed while the nonlocality can increase the minimal wave speed.
Wan-Tong Li: Supported by NNSF of China (10571078) and the Teaching and Research Award Program for Outstanding Young Teachers
in Higher Education Institutions of Ministry of Education of China. 相似文献
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We analyze the well-posedness of the initial value problem for the dissipative quasi-geostrophic equations in the subcritical
case. Mild solutions are obtained in several spaces with the right homogeneity to allow the existence of self-similar solutions.
While the only small self-similar solution in the strong
space is the null solution, infinitely many self-similar solutions do exist in weak-
spaces and in a recently introduced [7] space of tempered distributions. The asymptotic stability of solutions is obtained
in both spaces, and as a consequence, a criterion of self-similarity persistence at large times is obtained. 相似文献
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Giovanni Cimatti 《Annali di Matematica Pura ed Applicata》2002,181(2):181-212
The stability of the stationary solution of the thermistor as a circuit element is studied using a Liapunov functional and
the Hale–LaSalle invariance principle. The asymptotic stability of a class of periodic solutions is also considered.
Received: November 22, 1999; in final form: May 23, 2001?Published online: May 29, 2002 相似文献
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Frank Müller 《Calculus of Variations and Partial Differential Equations》2002,15(2):257-288
This paper deals with systems , , where the right hand side is a -valued, real analytic function. We prove that a solution of such a system can be continued across a straight line segment , if one prescribe certain nonlinear, mixed boundary conditions on , which are assumed to be real analytic too. This continuation will be constructed by solving certain hyperbolic initial boundary
value problems, generalizing an idea of H. Lewy. We apply this result to surfaces of prescribed mean curvature and to minimal
surfaces in Riemannian manifolds spanned into a regular Jordan curve : Supposing analyticity of all data, we show that both types of surfaces can be continued across .
Received: 29 December 2000 / Accepted: 11 July 2001 / Published online: 29 April 2002 相似文献
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C. Sparber J. A. Carrillo J. Dolbeault P. A. Markowich 《Monatshefte für Mathematik》2004,141(3):237-257
We analyze the long-time behavior of transport equations for a class of dissipative quantum systems with Fokker-planck type diffusion operator, subject to confining potentials of harmonic oscillator type. We establish the existence and uniqueness of a non-equilibrium steady state for the corresponding dynamics. Further, using a (classical) convex Sobolev inequality, we prove an optimal exponential rate of decay towards this state and additionally give precise dispersion estimates in those cases, where no stationary state exists. 相似文献
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Juan Manfredi Arshak Petrosyan Henrik Shahgholian 《Calculus of Variations and Partial Differential Equations》2002,14(3):359-384
We consider a free boundary problem for the p-Laplacian
describing nonlinear potential flow past a convex profile K with prescribed pressure on the free stream line. The main purpose of this paper is to study the limit as of the classical solutions of the problem above, existing under certain convexity assumptions on a(x). We show, as one can expect, that the limit solves the corresponding potential flow problem for the -Laplacian
in a certain weak sense, strong enough however, to guarantee uniqueness. We show also that in the special case the limit is given by the distance function.
Received: 10 October 2000 / Accepted: 23 February 2001 / Published online: 19 October 2001 相似文献
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Hideo Kozono 《Mathematische Annalen》2001,320(4):709-730
Consider the nonstationary Stokes equations in exterior domains with the compact boundary . We show first that the solution decays like for all as . This decay rate is optimal in the sense that for some as occurs if and only if the net force exerted by the fluid on is zero.
Received: 15 June 2000 / Published online: 18 June 2001 相似文献
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We introduce a new concept of solution for the Dirichlet problem for quasilinear parabolic equations in divergent form for
which the energy functional has linear growth. Using Kruzhkov's method of doubling variables both in space and time we prove
uniqueness and a comparison principle in for these solutions. To prove the existence we use the nonlinear semigroup theory.
Received: 26 October 2000 / Revised version: 1 May 2001 / Published online: 24 September 2001 相似文献