共查询到20条相似文献,搜索用时 15 毫秒
1.
Hua-Huai Chern Jong-Shenq Guo Chu-Pin Lo 《Proceedings of the American Mathematical Society》2003,131(10):3191-3201
We study a two-point free boundary problem for the curvature flow equation. By studying the corresponding nonlinear initial value problem, we obtain the existence and uniqueness of the forward self-similar solution of this problem. The corresponding curve is called the self-similar expanding curve. We also derive the asymptotic stability of this curve.
2.
We investigate computability of a self-similar set on a Euclidean space. A nonempty compact subset of a Euclidean space is called a self-similar set if it equals to the union of the images of itself by some set of contractions. The main result in this paper is that if all of the contractions are computable, then the self-similar set is a recursive compact set. A further result on the case that the self-similar set forms a curve is also discussed. 相似文献
3.
In this paper, we consider self-similar solutions for an anisotropic curvature flow equation in the plane. For some (nonsymmetric)
interfacial energy, we show that there exists a self-similar curve which is not a local minimizer of the entropy under the
area constraint. As its result, we obtain non-uniqueness of self-similar solutions for the anisotropic flow. 相似文献
4.
Tai-Chia Lin Chi-Cheung Poon Dong-Ho Tsai 《Calculus of Variations and Partial Differential Equations》2009,34(2):153-178
We study the evolution driven by curvature of a given convex immersed closed plane curve. We show that it will converge to
a self-similar solution eventually. This self-similar solution may or may not contain singularities. In case it does, we also
have estimate on the curvature blow-up rate. 相似文献
5.
This paper deals with the critical curve for a nonlinear boundary value problem of a fast diffusive non-Newtonian system. We first obtain the critical global existence curve by constructing the self-similar supersolution and subsolution. And then the critical Fujita curve is conjectured with the aid of some new results. 相似文献
6.
This paper is concerned with the critical curves of a degenerate parabolic equation with a source and nonlinear boundary flux. We obtain the critical global existence curve and critical Fujita curve by constructing various self-similar supersolutions and subsolutions. 相似文献
7.
本文讨论一类(包括Koch曲线在内的)自相似曲线,证明了其上的简单曲线是Whitney型临界集,并在微小扰动下仍是简单曲线. 相似文献
8.
This article deals with the critical curve of a fast diffusive polytropic filtration system coupled at the boundary condition. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical curve of Fujita type is conjectured with the aid of some new results. 相似文献
9.
We consider solutions of the Navier-Stokes equations in 3d with vortex filament initial data of arbitrary circulation, that is, initial vorticity given by a divergence-free vector-valued measure of arbitrary mass supported on a smooth curve. First, we prove global well-posedness for perturbations of the Oseen vortex column in scaling-critical spaces. Second, we prove local well-posedness (in a sense to be made precise) when the filament is a smooth, closed, non-self-intersecting curve. Besides their physical interest, these results are the first to give well-posedness in a neighborhood of large self-similar solutions of 3d Navier-Stokes, as well as solutions that are locally approximately self-similar. © 2023 Wiley Periodicals LLC. 相似文献
10.
This paper deals with the critical curve of the non-Newtonian polytropic filtration equation coupled via nonlinear boundary flux. The critical global existence curve is obtained by constructing various self-similar supersolutions and subsolutions. Furthermore, we get some new results on the critical Fujita curve. 相似文献
11.
The notion of finite-type open set condition is defined to calculate the Hausdorff dimensions of the sections of some self-similar sets, such as the dimension of intersection of the Koch curve and the line x = a with a∈Q. 相似文献
12.
考虑了一个具有多重非线性的抛物模型中,非线性扩散项、非线性反应项和非线性边界流三种非线性机制之间的相互作用.通过构造自相似上解和自相似下解,获得了临界整体存在性曲线和临界Fujita曲线. 相似文献
13.
This article deals with the critical curves for a degenerate parabolic system coupled via nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve. The critical curve of Fujita type is conjectured with the aid of some new results. 相似文献
14.
15.
Zhongping Li Chunlai Mu Zejian Cui 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,7(4):284-298
This paper deals with the critical curves of the fast diffusive polytropic filtration equations coupled via nonlinear boundary
flux. By constructing self-similar super and sub solutions we obtain the critical global existence curve. The critical curve
of Fujita type is conjectured with the aid of some new results. 相似文献
16.
Zhongping Li Chunlai Mu Zejian Cui 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(2):284-298
This paper deals with the critical curves of the fast diffusive polytropic filtration equations coupled via nonlinear boundary
flux. By constructing self-similar super and sub solutions we obtain the critical global existence curve. The critical curve
of Fujita type is conjectured with the aid of some new results.
相似文献
17.
Jun Ai Kai-Seng Chou Juncheng Wei 《Calculus of Variations and Partial Differential Equations》2001,13(3):311-337
Similarity between the roles of the group on the equation for self-similar solutions of the anisotropic affine curve shortening problem and of the conformal group
of on the Nirenberg problem for prescribed scalar curvature is explored. Sufficient conditions for the existence of affine self-similar
curves are established.
Received June 26, 1999 / Accepted January 28, 2000 / Published online December 8, 2000 相似文献
18.
In this paper, we consider the existence and non-existence of global solutions of the non-Newtonian polytropic filtration equations with nonlinear boundary conditions. We first obtain the critical global existence curve by constructing various self-similar supersolutions and subsolutions. And then the critical Fujita curve is conjectured with the aid of some new results. 相似文献
19.
This article deals with the degenerate parabolic system with nonlinear boundary flux. By constructing the self-similar supersolution and subsolution, we obtain the critical global existence curve and the critical Fujita curve for the problem. Especially for the blow-up case, it is rather technical. It comes from the construction of the so-called Zel’dovich-Kompaneetz-Barenblatt profile. 相似文献
20.
We construct a random walk model on sets with self-similar structure parametrized by a real line. The model in particular explains the arising nonlinearity with respect to the mean square time in the so-called anomalous transports. 相似文献