共查询到20条相似文献,搜索用时 250 毫秒
1.
Ar. S. Tersenov 《Siberian Mathematical Journal》2016,57(5):918-928
We consider the Dirichlet problem for the inhomogeneous p-Laplace equation with p nonlinear source. New sufficient conditions are established for the existence of weak bounded radially symmetric solutions as well as a priori estimates of solution and of the gradient of solution. We obtain an explicit formula that shows the dependence of the existence of these solutions on the dimension of the problem, the size of the domain, the exponent p, the nonlinear source, and the exterior mass forces. 相似文献
2.
E. I. Galakhov 《Proceedings of the Steklov Institute of Mathematics》2013,283(1):35-43
Using a modification of the nonlinear capacity method, we obtain necessary conditions for the solvability of some nonlinear partial differential equations and inequalities containing the polyharmonic operator and terms that depend on the norm of the gradient of the solution, both in the entire space and in bounded domains; in the latter case the coefficients of the inequality are allowed to have singularities. 相似文献
3.
É. I. Abduragimov 《Mathematical Notes》2016,100(5-6):649-659
Sufficient conditions for the existence and uniqueness of a positive radially symmetric solution of the Dirichlet problem for a nonlinear elliptic second-order system with p-Laplacian are obtained. In addition, it also proved that these conditions guarantee the nonexistence of a global positive radially symmetric solution. 相似文献
4.
P. Poláčik 《偏微分方程通讯》2013,38(11):1615-1638
We consider nonautonomous quasilinear parabolic equations satisfying certain symmetry conditions. We prove that each positive bounded solution u on ? N × (?∞, T) decaying to zero at spatial infinity uniformly with respect to time is radially symmetric around some origin in ? N . The origin depends on the solution but is independent of time. We also consider the linearized equation along u and prove that each bounded (positive or not) solution is a linear combination of a radially symmetric solution and (nonsymmetric) spatial derivatives of u. Theorems on reflectional symmetry are also given. 相似文献
5.
E. I. Abduragimov 《Russian Mathematics (Iz VUZ)》2011,55(10):1-8
We obtain sufficient conditions for the existence of a unique positive radially symmetric solution to the Dirichlet problem
for a quasilinear equation of elliptic type in a multidimensional ball. 相似文献
6.
ONINITIAL BOUNDARYVALUEPROBLEMSFORNONLINEARSCHRDINGEREQUATIONS¥LiYongsheng(李用声)ChenQingyi(陈庆益)(Dept.ofMath.,HuazhongUnv.ofSci... 相似文献
7.
In this paper we present an elementary theory about the existence of eigenvalues for fully nonlinear radially symmetric 1-homogeneous operators. A general theory for first eigenvalues and eigenfunctions of 1-homogeneous fully nonlinear operators exists in the framework of viscosity solutions. Here we want to show that for the radially symmetric operators or in the one dimensional case a much simpler theory, based on ode and degree theory arguments, can be established. We obtain the complete set of eigenvalues and eigenfunctions characterized by the number of zeroes. 相似文献
8.
We study the isentropic compressible Navier–Stokes equations with radially symmetric data in an annular domain. We first prove the global existence and regularity results on the radially symmetric weak solutions with non‐negative bounded densities. Then we prove the global existence of radially symmetric strong solutions when the initial data ρ0, u 0 satisfy the compatibility condition for some radially symmetric g ∈ L2. The initial density ρ0 needs not be positive. We also prove some uniqueness results on the strong solutions. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
9.
Monica Marras Stella Vernier Piro 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,203(1):766-779
We investigate the behavior of the solution of a nonlinear heat problem, when Robin conditions are prescribed on the boundary
∂Ω × (t > 0), Ω a bounded R
2 domain. We determine conditions on the geometry and data sufficient to preclude the blow up of the solution and to obtain
an exponential decay bound for the solution and its gradient. 相似文献
10.
P. Poláčik 《偏微分方程通讯》2013,38(11):1567-1593
We consider quasilinear parabolic equations on ? N satisfying certain symmetry conditions. We prove that bounded positive solutions decaying to zero at spatial infinity are asymptotically radially symmetric about a center. The asymptotic center of symmetry is not fixed a priori (and depends on the solution) but it is independent of time. We also prove a similar theorem on reflectional symmetry. 相似文献
11.
Alessandra Lunardi 《偏微分方程通讯》2013,38(1):145-172
We consider a class of intial boudnary value problems for parabolic equaitons of the form u$sub:t$esub:=f(t,x,u,Du,au) in a bounded domain Ω where A is an elliptic operator with continous coefficients. Scuh problems can be modeled by nonlinear evolation equaitons in Banach spaces, and we use abstract parabolic equairtions technique to show existence, uniqueness, regularity of a local solution, and to give sufficient conditions for existence in the large. In particular, we don't need growth assumptions on f with respect to Au to get existence in the large. In the case where Ω is a ball, A=D and f=f(t,|x||Du|2, Du) we show that the solution is radially symmetric if the initial value is 相似文献
12.
Monica Marras Stella Vernier Piro 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(5):766-779
We investigate the behavior of the solution of a nonlinear heat problem, when Robin conditions are prescribed on the boundary
∂Ω × (t > 0), Ω a bounded R
2 domain. We determine conditions on the geometry and data sufficient to preclude the blow up of the solution and to obtain
an exponential decay bound for the solution and its gradient.
Supported by the University of Cagliari. 相似文献
13.
In this paper, we investigate the symmetry of integral equation systems with Bessel kernel on bounded domains. Under some natural integrability conditions, we prove that the domains are balls and all positive solutions are radially symmetric and monotonic decreasing. 相似文献
14.
A Note on C1,α Estimates for Solutions of Fully Nonlinear Elliptic Equations and Obstacle Problems
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Chen Yazhe 《偏微分方程(英文版)》1992,5(4):1-12
We deal with C^{1,α} interior estimates for solutions of fully nonlinear equation F(D²u, Du, x) = f(x) with the bounded gradient Du and a bounded f(x). Based on these estimates we obtain the existence of strong solutions of the obstacle problem for fully nonlinear elliptic equations under natural structure conditions. 相似文献
15.
Xiaotao Huang Dongsheng Li Lihe Wang 《Journal of Mathematical Analysis and Applications》2011,376(2):443-450
In this paper, we investigate the symmetry of domains and solutions of integral equation systems on bounded domains. Under some natural integrability conditions, we prove that the domains are balls, all positive solutions of systems are radially symmetric and monotone decreasing with respect to the radius. 相似文献
16.
Siberian Mathematical Journal - We construct new radially symmetric exact solutions of the multidimensional nonlinear diffusion equation, which can be expressed in terms of elementary functions,... 相似文献
17.
Spherically Symmetric Solutions to Compressible Hydrodynamic Flow of Liquid Crystals in N Dimensions
The paper is concerned with the system modeling the compressible hydrodynamic flow of liquid crystals with radially symmetric initial data and non-negative initial density in dimension N (N ≥ 2).The au... 相似文献
18.
A. I. Perov 《Differential Equations》2012,48(5):670-680
We obtain new conditions for the existence of bounded solutions of higher-order nonlinear differential equations. In addition to the classical contraction mapping principle, A.N. Tikhonov’s fixed-point principle is used in the proof of existence theorems. Assertions dealing with the stability of a bounded solution are derived directly from the corresponding results obtained by M.A. Krasnosel’skii and A.V. Pokrovskii. 相似文献
19.
Miroslav Engliš 《复变函数与椭圆型方程》2015,60(12):1712-1726
We obtain a formula for the Sobolev inner product in standard weighted Bergman spaces of holomorphic functions on a bounded symmetric domain in terms of the Peter–Weyl components in the Hua–Schmidt decomposition, and use it to clarify the relationship between the analytic continuation of these standard weighted Bergman spaces and the Sobolev spaces on bounded symmetric domains. 相似文献
20.
Ahmad Z. Fino Mustapha Jazar 《Nonlinear Analysis: Theory, Methods & Applications》2012,75(6):3122-3129
We consider the Cauchy problem for second-order nonlinear ordinary differential inequalities with a nonlinear memory term. We obtain blow-up results under some conditions on the initial data. We also give an application to a semilinear hyperbolic equation in a bounded domain. 相似文献