共查询到20条相似文献,搜索用时 31 毫秒
1.
We study asymptotic behavior in time of small solutions to nonlinear heat equations in subcritical case. We find a new family of self-similar solutions which change a sign. We show that solutions are stable in the neighborhood of these self-similar solutions. 相似文献
2.
Ryuji Kajikiya 《Journal of Differential Equations》2018,264(2):786-834
In the present paper, we study the initial boundary value problem of the sublinear parabolic equation. We prove the existence of solutions and investigate the stability and instability of stationary solutions. We show that a unique positive and a unique negative stationary solutions are exponentially stable and give the exact exponent. We prove that small stationary solutions are unstable. For one space dimensional autonomous equations, we elucidate the structure of stationary solutions and study the stability of all stationary solutions. 相似文献
3.
Marta Mazzocco 《Mathematische Annalen》2001,321(1):157-195
We study the solutions of a particular family of Painlevé VI equations with parameters and , for . We show that in the case of half-integer , all solutions can be written in terms of known functions and they are of two types: a two-parameter family of solutions
found by Picard and a new one-parameter family of classical solutions which we call Chazy solutions. We give explicit formulae
for them and completely determine their asymptotic behaviour near the singular points and their nonlinear monodromy. We study the structure of analytic continuation of the solutions to the PVI equation for any such that . As an application, we classify all the algebraic solutions. For half-integer, we show that they are in one to one correspondence with regular polygons or star-polygons in the plane. For
integer, we show that all algebraic solutions belong to a one-parameter family of rational solutions.
Received: 23 February 1999 / Accepted: 10 January 2001 / Published online: 18 June 2001 相似文献
4.
《Chaos, solitons, and fractals》2000,11(1-3):53-71
In this paper, we construct hierarchies of rational solutions of the discrete third Painlevé equation (d-PIII) by applying Schlesinger transformations to simple initial solutions. We show how these solutions reduce in the continuous limit to the hierarchies of rational solutions of the third Painlevé equation (PIII). We also study the solutions of d-PIII which are expressed in terms of discrete Bessel functions and show that these solutions reduce in the continuous limit the hierarchies of special function solutions of PIII. 相似文献
5.
We study the solutions to the Landau–Lifshitz system in a bilayered ferromagnetic body when super-exchange and surface anisotropy interactions are present at the interface between the layers. We prove the existence of weak solutions in infinite time and strong solutions in finite time. 相似文献
6.
Vladimir I. Bogachev Michael Röckner Stanislav V. Shaposhnikov 《Journal of Functional Analysis》2019,276(12):3681-3713
We study convergence in variation of probability solutions of nonlinear Fokker–Planck–Kolmogorov equations to stationary solutions. We obtain sufficient conditions for the exponential convergence of solutions to the stationary solution in case of coefficients that can have an arbitrary growth at infinity and depend on the solutions through convolutions with unbounded discontinuous kernels. In addition, we study a more difficult case where the nonlinear equation has several stationary solutions and convergence to a stationary solution depends on initial data. Finally, we obtain sufficient conditions for solvability of nonlinear Fokker–Planck–Kolmogorov equations. 相似文献
7.
In this paper, we study the wave-breaking phenomena and global existence for the generalized two-component Hunter–Saxton system in the periodic setting. We first establish local well-posedness for the generalized two-component Hunter–Saxton system. We obtain a wave-breaking criterion for solutions and results of wave-breaking solutions with certain initial profiles. We also determine the exact blow-up rate of strong solutions. Finally, we give a sufficient condition for global solutions. 相似文献
8.
We consider the problem on bifurcations of periodic solutions near triangular libration points in the plane elliptic bounded
three-body problem. We determine values of the mass parameter such that at small values of the eccentricity the problem has
non-stationary periodic solutions close to a libration point. We determine bifurcation types and study the asymptotic formulas
for the mentioned solutions. 相似文献
9.
José M. Arrieta Neus Cónsul Anibal Rodríguez-Bernal 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,23(2):1-14
We prove the existence of nonconstant stable stationary
solutions of
an evolution problem with a nonlinear reaction acting on the
boundary. These solutions present layers at certain points of the
boundary. We also study the behavior of these solutions as the small
parameter appearing in the equation approaches zero and show some
stability properties of the profiles given by these equilibrium
solutions. 相似文献
10.
Liangwen Liao 《Journal of Mathematical Analysis and Applications》2005,309(1):91-102
We study the properties of meromorphic solutions of the Schwarzian differential equations in the complex plane by using some techniques from the study of the class Wp. We find some upper bounds of the order of meromorphic solutions for some types of the Schwarzian differential equations. We also show that there are no wandering domains nor Baker domains for meromorphic solutions of certain Schwarzian differential equations. 相似文献
11.
Shuji Machihara 《Journal of Mathematical Analysis and Applications》2003,281(2):552-564
We study the inviscid limit of the complex Ginzburg-Landau equation. We observe that the solutions for the complex Ginzburg-Landau equation converge to the corresponding solutions for the nonlinear Schrödinger equation. We give its convergence rate. We estimate the integral forms of solutions for two equations. 相似文献
12.
《Indagationes Mathematicae》2017,28(2):601-611
We study qualitative properties of solutions of an integral equation associated the Benjamin–Ono–Zakharov–Kuznetsov operator. We establish the regularity of the positive solutions without the assumption of being in fractional Sobolev–Liouville spaces. Moreover we show that the solutions are axially symmetric. Furthermore we establish Lipschitz continuity and the decay rate of the solutions. 相似文献
13.
We prove the existence of nonconstant stable stationary
solutions of
an evolution problem with a nonlinear reaction acting on the
boundary. These solutions present layers at certain points of the
boundary. We also study the behavior of these solutions as the small
parameter appearing in the equation approaches zero and show some
stability properties of the profiles given by these equilibrium
solutions. 相似文献
14.
A. Polishchuk 《Advances in Mathematics》2002,168(1):56-95
We show that elliptic solutions of classical Yang-Baxter equation (CYBE) can be obtained from triple Massey products on an elliptic curve. We introduce the associative version of this equation which has two spectral parameters and construct its elliptic solutions. We also study some degenerations of these solutions. 相似文献
15.
Abdul‐Majid Wazwaz 《Mathematical Methods in the Applied Sciences》2017,40(6):2277-2283
In this work, we study the two‐mode Korteweg–de Vries (TKdV) equation, which describes the propagation of two different waves modes simultaneously. We show that the TKdV equation gives multiple soliton solutions for specific values of the nonlinearity and dispersion parameters involved in the equation. We also derive other distinct exact solutions for general values of these parameters. We apply the simplified Hirota's method to study the specific of the parameters, which gives multiple soliton solutions. We also use the tanh/coth method and the tan/cot method to obtain other set of solutions with distinct physical structures. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
16.
A. Castro 《Advances in Mathematics》2010,225(4):1820-1829
We study the formation of singularities of a 1D non-linear and non-local equation. We show that this equation provides solutions of the surface quasi-geostrophic equation with infinite energy. The existence of self-similar solutions and the blow-up for classical solutions are shown. 相似文献
17.
Jiuli Yin Lixin TianXinghua Fan 《Communications in Nonlinear Science & Numerical Simulation》2012,17(3):1224-1232
Different kinds of optical wave solutions to the nonlinearly dispersive Schrödinger equation are given according to different parameters’ regions. Those solutions include looped wave solutions, cusped wave solutions, peaked wave solutions, compacted wave solutions. The looped and cusped forms have not been reported in the literature regarding to the study of the nonlinear Schrödinger equation. We also study the limiting behavior of all periodic solutions as the parameters trend to some special values. 相似文献
18.
Juan Casado-Díaz 《Journal of Mathematical Analysis and Applications》2007,328(1):151-169
We study the asymptotic behavior at infinity of the solutions of a nonlinear elliptic system posed in a cylinder of infinite length. The problem is written in a variational formulation, where we ask the derivative of the solutions to be in Lp. We show that an exponential decay at infinity for the second member implies exponential decay for the derivative of the solutions. We also give an application of this result to the study of boundary layers problems. 相似文献
19.
We study a nonlinear reaction-diffusion system that is modeled by a system of parabolic equations with power-law nonlinear terms. The proposed construction of exact solutions enables us to split the process of finding the components depending on time and the spatial coordinates. We construct multiparametric families of exact solutions in elementary functions. The cases are elaborated of blow-up solutions as well as exact solutions time-periodic but spatially anisotropic. 相似文献
20.
研究了一类趋化性生物模型行波解的存在性和正则性.通过直接计算得到了其行波解存在的充分必要条件;在一定条件下,研究了行波解的正则与非正则的性质;在特殊情形下给出了行波解的显式解. 相似文献