共查询到20条相似文献,搜索用时 15 毫秒
1.
In this note, we prove an ?‐regularity theorem for the Ricci flow. Let (Mn,g(t)) with t ? [?T,0] be a Ricci flow, and let Hx0(y,s) be the conjugate heat kernel centered at some point (x0,0) in the final time slice. By substituting Hx0(?,s) into Perelman's W‐functional, we obtain a monotone quantity Wx0(s) that we refer to as the pointed entropy. This satisfies Wx0(s) ≤ 0, and Wx0(s) = 0 if and only if (Mn,g(t)) is isometric to the trivial flow on Rn. Then our main theorem asserts the following: There exists ? > 0, depending only on T and on lower scalar curvature and μ‐entropy bounds for the initial slice (Mn,g(?T)) such that Wx0(s) ≥ ?? implies |Rm| ≤ r?2 on P? r(x0,0), where r2 ≡ |s| and Pρ(x,t) ≡ Bρ(x,t) × (t?ρ2,t] is our notation for parabolic balls. The main technical challenge of the theorem is to prove an effective Lipschitz bound in x for the s‐average of Wx(s). To accomplish this, we require a new log‐Sobolev inequality. Perelman's work implies that the metric measure spaces (Mn,g(t),dvolg(t)) satisfy a log‐Sobolev; we show that this is also true for the heat kernel weighted spaces (Mn,g(t),Hx0(?,t)dvolg(t)). Our log‐Sobolev constants for these weighted spaces are in fact universal and sharp. The weighted log‐Sobolev has other consequences as well, including certain average Gaussian upper bounds on the conjugate heat kernel. © 2014 Wiley Periodicals, Inc. 相似文献
2.
该文利用Krasnoselskii不动点定理和Schwarz不等式, 获得了关于非自治的广义单种群Logistic模型
x=x(t){a(t)-b(t)x(t)-∑ni=1ci (t)x(t-τi(t))-∫0-∞k(t, s)x(t+s)ds}
的正周期解的存在性和唯一性的一些新的结果. 相似文献
3.
A coupled non-linear hyperbolic-sobolev system 总被引:1,自引:0,他引:1
Richard E. Ewing 《Annali di Matematica Pura ed Applicata》1977,114(1):331-349
Summary A boundary-initial value problem for a quasilinear hyperbolic system in one space variable is coupled to a boundary-initial
value problem for a quasilinear equation of Sobolev type in two space variables of the form Mut(x, t)+L(t) u (x, t)=f(x, t, u(x, t)) where M and L(t) are second order elliptic spacial operators. The coupling occurs through
one of the boundary conditions for the hyperbolic system and the source term in the equation of Sobolev type. Such a coupling
can arise in the consideration of oil flowing in a fissured medium and out of that medium via a pipe. Barenblatt, Zheltov,
and Kochina[2] have modeled flow in a fissured medium via a special case of the above equation. A local existence and uniqueness theorem
is demonstrated. The proof involves the method of characteristics, some applications of results of R. Showalter and the contraction
mapping theorem.
Entrata in Redazione il 28 luglio 1976. 相似文献
4.
G. Anichini 《Journal of Optimization Theory and Applications》1980,32(2):183-199
In this paper, we establish sufficient conditions upon the functionsA(t, x),B(t),g(t, x, u), such that the nonlinear control process $$x' = A(t,x)x + B(t)u + g(t,x,u)$$ is completely controllable and it is possible to control not only the statex of the system, but also its velocityx′. The method used is a transformation of the given control system into a boundary-value problem similar to one considered by Lukes on perturbed linear control systems. The main tool used is Schaefer's fixed-point argument. 相似文献
5.
GLOBAL ATTRACTIVITY IN AGENERALIZED DELAY LOGISTIC EQUATION 总被引:7,自引:0,他引:7
LIJINGWEN 《高校应用数学学报(英文版)》1996,11(2):165-174
Abstract.Based on the literature 相似文献
6.
M. N. Manougian A. N. V. Rao C. P. Tsokos 《Annali di Matematica Pura ed Applicata》1976,110(1):211-222
The aim of the present paper is to study a nonlinear stochastic integral equation of the form
x(t; w) = h(t, x(t; w)) + \mathop \smallint 0t k1 (t, t; w)f1 (t, x(t; w))dt+ \mathop \smallint 0t k2 (t, t; w)f2 (t, x(t; w))db(t; w)x(t; \omega ) = h(t, x(t; \omega )) + \mathop \smallint \limits_0^t k_1 (t, \tau ; \omega )f_1 (\tau , x(\tau ; \omega ))d\tau + \mathop \smallint \limits_0^t k_2 (t, \tau ; \omega )f_2 (\tau , x(\tau ; \omega ))d\beta (\tau ; \omega ) 相似文献
7.
D. Bothe 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1999,114(1):779-808
We study the differential equation x"+g(x¢)+m(x) sgn x¢+f(x)=j(t)x''+g(x')+\mu(x)\,{\rm sgn}\, x'+f(x)=\varphi(t) with T-periodic right-hand side, which models e.g. a mechanical system with one degree of freedom subjected to dry friction and periodic external force. If, in particular, the damping term g is present and acts, up to a bounded difference, like a linear damping, we get existence of a T-periodic solution.¶In the more difficult case g = 0, we concentrate on the model equation x"+m(x) sgn x¢+x=j(t)x''+\mu(x)\,{\rm sgn}\,x'+x=\varphi(t) and obtain sufficient conditions for the existence of a T-periodic solution by application of Brouwer's fixed point theorem. For this purpose we show that a certain associated autonomous differential equation admits a periodic orbit such that the surrounded set (minus some neighborhood of the equilibria) is forward invariant for the equation above. Under additional assumptions on 7 we prove boundedness of all solutions.¶Finally, we provide a principle of linearized stability for periodic solutions without deadzones, where the "linearized" differential equation is an impulsive Hill equation. 相似文献
8.
This paper examines the existence and uniqueness of solutions for the fractional boundary value problems with integral boundary conditions. Banach’s contraction mapping principle and Schaefer’s fixed point theorem have been used besides topological technique of approximate solutions. An example is propounded to uphold our results. 相似文献
9.
Mitsuhiro Nakao 《Journal of Differential Equations》1982,44(1):63-81
A simple result concerning integral inequalities enables us to give an alternative proof of Waltman's theorem: limt → ∞ ∝t0a(s) ds = ∞ implies oscillation of the second order nonlinear equation y″(t) + a(t) f(y(t)) = 0; to prove an analog of Wintner's theorem that relates the nonoscillation of the second order nonlinear equations to the existence of solutions of some integral equations, assuming that limt → ∞ ∝t0a(s) ds exists; and to give an alternative proof and to extend a result of Butler. An often used condition on the coefficient a(t) is given a more familiar equivalent form and an oscillation criterion involving this condition is established. 相似文献
10.
The existence of positive solutions of the Fredholm nonlinear equation y(t) = h(t) + ∫T0k(t, s)[f(y(s)) + g(y(s))] ds is discussed. It is assumed that f is a continuous, nondecreasing function and g is continuous, nonincreasing, and possibly singular. 相似文献
11.
Tibor Krisztin 《Periodica Mathematica Hungarica》2008,56(1):83-95
In this survey paper the delay differential equation (t) = −μx(t) + g(x(t − 1)) is considered with μ ≥ 0 and a smooth real function g satisfying g(0) = 0. It is shown that the dynamics generated by this simple-looking equation can be very rich. The dynamics is completely
understood only for a small class of nonlinearities. Open problems are formulated.
Supported in part by the Hungarian NFSR, Grant No. T049516. 相似文献
12.
This paper deals with a class of localized and degenerate quasilinear parabolic systems
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