首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
In this paper we study the Cauchy problem for the singular evolution p-Laplacian equations with gradient term and source on the assumption of measures as initial conditions. For the supercritical case q>p−1+p/N, we obtain that for every nonnegative solution there exists a nonnegative Radon measure μ as initial trace and μ has some local regularity.  相似文献   

3.
4.
5.
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   

6.
7.
Motivated by a recent curvature flow introduced by Professor S.-T. Yau [S.-T. Yau, Private communication on his “Curvature Difference Flow”, 2007], we use a simple curvature flow to evolve a convex closed curve to another one (under the assumption that both curves have the same length). We show that, under the evolution, the length is preserved and if the curvature is bounded above during the evolution, then an initial convex closed curve can be evolved to another given one.  相似文献   

8.
We bound the modulus of continuity of solutions to quasilinear parabolic equations in one space variable in terms of the initial modulus of continuity and elapsed time. In particular we characterize those equations for which the Lipschitz constants of solutions can be bounded in terms of their initial oscillation and elapsed time.  相似文献   

9.
We show that weak solutions to a singular parabolic partial differential equation globally belong to a higher Sobolev space than assumed a priori. To this end, we prove that the gradients satisfy a reverse Hölder inequality near the boundary. The results extend to singular parabolic systems as well. Motivation for studying reverse Hölder inequalities comes partly from applications to regularity theory.  相似文献   

10.
The problem of existence of time-periodic solutions for the time-dependent Ginzburg-Landau equations of superconductivity is discussed. It is assumed that the applied magnetic field H is -periodic in time, and so is the associated dynamical process. We prove the existence of -periodic solutions in time, which are exactly the fixed points of the associated period mapping.  相似文献   

11.
We study a parabolic version of a system of Von Karman type on a compact Kähler manifold of arbitrary dimension. We provide local in time regular solutions, which can be extended to global bounded ones if the data of the problem are small.  相似文献   

12.
In this paper we derive the first and second variations for a nonlinear time scale optimal control problem with control and state-endpoints equality constraints. Using the first variation, a first order necessary condition for weak local optimality is obtained under the form of a weak maximum principle generalizing the Dubois–Reymond Lemma to the optimal control setting and time scales. A second order necessary condition in terms of the accessory problem is derived by using the nonnegativity of the second variation at all admissible directions. The control problem is studied under a controllability assumption, and with or without the shift in the state variable. These two forms of the problem are shown to be equivalent.  相似文献   

13.
We complete the study of a parabolic version of a system of Von Karman type on a compact Kähler manifold of complex dimension m. We consider a family of problems k(P). We prove existence of local in time solutions when k=0. When −m?k<0, we define a notion of weak solution, and give some uniqueness and existence results.  相似文献   

14.
The local well-posedness for the generalized two-dimensional (2D) Ginzburg-Landau equation is obtained for initial data in Hs(R2)(s>1/2). The global result is also obtained in Hs(R2)(s>1/2) under some conditions. The results on local and global well-posedness are sharp except the endpoint s=1/2. We mainly use the Tao's [k;Z]-multiplier method to obtain the trilinear and multilinear estimates.  相似文献   

15.
We show that a nontrivial homothetic self-similar solution can happen only when F(k)=kα or F(k)=−kα. We also derive a parametric representation of a translational self-similar solution. A translational self-similar solution may have self-intersections but cannot be a simple closed curve for any F(k).  相似文献   

16.
17.
In this paper we study some criteria for the full (space-time) regularity of weak solutions to the Navier-Stokes equations. In particular, we generalize some classical and very recent criteria involving the velocity, or its derivatives. More specifically, we show with elementary tools that if a weak solution, or its vorticity, is small in appropriate Marcinkiewicz spaces, then it is regular.  相似文献   

18.
19.
This paper deals with the blow-up for a system of semilinear r-Laplace heat equations with nonlinear boundary flux. It is shown that, under certain conditions on the nonlinearities and data, blow-up will occur at some finite time, and when blow-up does occur upper and lower bounds for the blow-up time are obtained.  相似文献   

20.
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号