共查询到20条相似文献,搜索用时 15 毫秒
1.
2.
3.
We prove existence and uniqueness of solutions of the Anisotropic Total Variation Flow when the initial data is an L2 function and we give a characterization of such solutions that allows us to find explicit evolutions of sets in the presence of an anisotropy.Mathematics Subject Classification (2000): 35k65, 35k55, 35k60 相似文献
4.
In this article, we investigate the hyperbolic geometry flow with time-dependent dissipation(?~2 g_(ij))/? t~2+μ/((1 + t)~λ)(? g_(ij))/? t=-2 R_(ij),on Riemann surface. On the basis of the energy method, for 0 λ≤ 1, μ λ + 1, we show that there exists a global solution gij to the hyperbolic geometry flow with time-dependent dissipation with asymptotic flat initial Riemann surfaces. Moreover, we prove that the scalar curvature R(t, x) of the solution metric g_(ij) remains uniformly bounded. 相似文献
5.
6.
7.
In this article, we investigate the lower bound of life-span of classical solutions of the hyperbolic geometry flow equations in several space dimensions with “small” initial data. We first present some estimates on solutions of linear wave equations in several space variables. Then, we derive a lower bound of the life-span of the classical solutions to the equations with “small” initial data. 相似文献
8.
9.
In this paper we give some sufficient conditions for ensuring the existence and uniqueness of a mild almost automorphic solution to a second-order semilinear evolution equation in a Banach space. We also present some properties of the (new) notion of a uniform spectrum of bounded functions. 相似文献
10.
11.
12.
《Nonlinear Analysis: Theory, Methods & Applications》2010,72(12):e432-e435
In this paper we give some sufficient conditions for ensuring the existence and uniqueness of a mild almost automorphic solution to a second-order semilinear evolution equation in a Banach space. We also present some properties of the (new) notion of a uniform spectrum of bounded functions. 相似文献
13.
Toka Diagana 《Communications in Nonlinear Science & Numerical Simulation》2012,17(11):4074-4084
In this paper we make extensive use of dichotomy tools and the well-known Schauder fixed point principle to study and obtain the existence of almost automorphic solutions to some nonautonomous damped second-order differential equations. To illustrate our abstract result, we study the existence of almost automorphic solutions to the so-called plate-like equation. 相似文献
14.
15.
In this paper, we first present a notion of almost periodic functions on time scales and study their basic properties. Then by means of Liapunov functionals, we study the existence of almost periodic solutions for an almost periodic dynamic equation on time scales. 相似文献
16.
This paper is concerned with the problem of explosive solutions for a class of stochastic differential equations. Our main results are presented as two theorems. Theorem 1 is concerned with the existence of explosive solutions with positive probability under certain sufficient conditions. With some additional mild conditions, it is shown in Theorem 2 that the explosion will occur almost surely. The methods of auxiliary functions and cycles are used in the proofs. Several remarks about their applications are given. 相似文献
17.
Jiang Xu 《Journal of Mathematical Analysis and Applications》2009,351(2):682-693
This paper mainly deals with the multidimensional hydrodynamic model for semiconductors. Inspired by the previous papers [Y. Shizuta, S. Kawashima, Systems of equations of hyperbolic-parabolic type with applications to the discrete Boltzmann equation, Hokkaido Math. J. 14 (1985) 249-275; S. Kawashima, W.-A. Yong, Dissipative structure and entropy for hyperbolic systems of balance laws, Arch. Ration. Mech. Anal. 174 (2004) 345-364; W.-A. Yong, Entropy and global existence for hyperbolic balance laws, Arch. Ration. Mech. Anal. 172 (2004) 247-266], we develop some new frequency-localization estimates to establish the global existence and exponential stability of (small) classical solutions in a class of critical Besov spaces, which are different from estimates in our recent paper [D.Y. Fang, J. Xu, T. Zhang, Global exponential stability of classical solutions to the hydrodynamic model for semiconductors, Math. Models Methods Appl. Sci. 17 (2007) 1507-1530]. Furthermore, this new method can also be applied to the multidimensional Euler equations with damping. The analytic tool used is the Littlewood-Paley decomposition. 相似文献
18.
Toka Diagana Gaston Nguerekata Nguyen Van Minh 《Proceedings of the American Mathematical Society》2004,132(11):3289-3298
This paper is concerned with the existence of almost automorphic mild solutions to equations of the form
where generates a holomorphic semigroup and is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to in terms of the imaginary spectrum of and the uniform spectrum of .
where generates a holomorphic semigroup and is an almost automorphic function. Since almost automorphic functions may not be uniformly continuous, we introduce the notion of the uniform spectrum of a function. By modifying the method of sums of commuting operators used in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to in terms of the imaginary spectrum of and the uniform spectrum of .
19.
20.
The method of upper and lower solutions is a classical tool in the theory of periodic differential equations of the second order. We show that this method does not have a direct extension to almost periodic equations. To do this we construct equations of this type without almost periodic solutions but having two constants as ordered upper and lower solutions. 相似文献