共查询到20条相似文献,搜索用时 15 毫秒
1.
Fei Liang 《Journal of Mathematical Analysis and Applications》2010,365(2):590-604
In this paper, we consider the asymptotic behavior for the degenerate nonlocal parabolic equation
2.
3.
Huashui Zhan 《Applications of Mathematics》2008,53(6):521-533
We study the large time asymptotic behavior of solutions of the doubly degenerate parabolic equation u
t
= div(u
m−1|Du|
p−2
Du) − u
q
with an initial condition u(x, 0) = u
0(x). Here the exponents m, p and q satisfy m + p ⩾ 3, p > 1 and q > m + p − 2.
The paper was supported by NSF of China (10571144), NSF for youth of Fujian province in China (2005J037) and NSF of Jimei
University in China. 相似文献
4.
This paper is devoted to the homogenization of a nonlinear degenerate parabolic problem ɑtu∈-div(D(x/∈, u∈,▽u∈)+ K(x/∈, u∈))= f(x) with Dirichlet boundary condition. Here the operator D(y, s,s) is periodic in y and degenerated in ▽s. In the paper, under the two-scale convergence theory, we obtain the limit equation as ∈→ 0 and also prove the corrector results of ▽u∈ to strong convergence. 相似文献
5.
The existence of solutions to a fourth-order p-Laplacian equation with boundary degeneracy is studied. For the purpose of solving the corresponding non-degenerate (with respect to the coefficient of fourth-order term) regularized problem, a fourth-order semi-discrete elliptic problem with homogeneous boundary conditions is established and its existence and uniqueness are obtained by the functional minimization method. It follows that the approximate solutions of the non-degenerate parabolic problem are constructed and the corresponding existence and uniqueness are discovered by a limit procedure from the energy estimation method and a compactness argument. Finally, the existence and regularity of solutions for the problem with boundary degeneracy is obtained by using a regularization parameter vanishing limit. 相似文献
6.
Zhaoyin Xiang 《Mathematical Methods in the Applied Sciences》2010,33(9):1078-1088
In this paper, we study the strict localization for the doubly degenerate parabolic equation with strongly nonlinear sources, We prove that, for non‐negative compactly supported initial data, the strict localization occurs if and only if q?m(p?1). Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
7.
YANG JINSHUN 《高校应用数学学报(英文版)》1995,10(2):155-166
ONTHECAUCHYPROBLEMOFNONLINEARDEGENERATEPARABOLICEQUATION¥YANGJINSHUNAbstract:Inthispaper,weprovetheexistenceofsolutionoftheCa... 相似文献
8.
The approximating character of solutions of a degenerate parabolicequation is studied in this paper. We will show that the solutionsare Lipschitz continuous with respect to the nonlinearitiesof the equations. An explicitly approximating estimate is obtained. 相似文献
9.
The global existence and finite time blow up of the positive solution for a nonlinear degenerate parabolic equation with non-local source are studied. 相似文献
10.
A complete upper estimate on the localization for the degenerate parabolic equation with nonlinear source
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This paper deals with the Cauchy problem for the degenerate parabolic equation with a strongly nonlinear source where N ≥ 1, p > 2, q ≥ p ? 1, and the blow‐up time T < ∞ . It has been shown that the solution u(x,t) is strictly localized for q ≥ p ? 1, provided that the initial function u0(x) has a compact support by Liang and Zhao. In addition, if q > 2p ? 1, an upper estimate on the localization in terms of the initial support and the blow‐up time T is partially derived by Liang. In this work, by using the De Giorgi‐type iteration technique, we give a complete estimate on the localization for all q ≥ p ? 1. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
11.
This paper is concerned with the well-posedness and asymptotic behavior of Dirichlet initial boundary value problem for a singular parabolic p-biharmonic equation with logarithmic nonlinearity. We establish the local solvability by the technique of cut-off combining with the methods of Faedo–Galerkin approximation and multiplier. Meantime, by virtue of the family of potential wells, we use the technique of modified differential inequality and improved logarithmic Sobolev inequality to obtain the global solvability, infinite and finite time blow-up phenomena, and derive the upper bound of blow-up time as well as the estimate of blow-up rate. Furthermore, the results of blow-up with arbitrary initial energy and extinction phenomena are presented. 相似文献
12.
Marin Slodi
ka 《Numerical Methods for Partial Differential Equations》2005,21(2):191-212
We study a nonlinear degenerate parabolic equation of the type accompanied by an initial datum and mixed boundary conditions. The symbol [ · ]+ denotes the usual cutoff function. The problem represents a model of a reactive solute transport in porous media. The exponent p fulfills p ∈ (0, 1). This limits the regularity of a solution and leads to inconveniences in the error analysis. We design a new robust linear numerical scheme for the time discretization. This is based on a suitable combination of the backward Euler method and a linear relaxation scheme. We prove the convergence of relaxation iterations on each time point ti. We derive the error estimates in suitable function spaces for all values of p ∈ (0, 1). © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005. 相似文献
13.
1.IntroductionWeareconcernedwiththesemigroupapproachtotheinitialvalueproblemfordoublynonlineardegenerateparabolicequationoftheformwhicharisesfromdifferentphysicalbackgroundssuchasthemodelingofthemotionofnon-Newtonianfluids.Inthepastyears,thenonlinear... 相似文献
14.
15.
In this paper, we study the initial-boundary value problem for a class of singular parabolic equations. Under some conditions, we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method. As a byproduct, we prove the existence of solutions to some problems with gradient terms, which blow up on the boundary. 相似文献
16.
In this article, it is shown that there exists a unique viscosity solution of the Cauchy problem for a degenerate parabolic equation with non-divergence form. 相似文献
17.
讨论了一类超抛物型方程的非线性奇摄动问题.首先引入了相应问题的比较定理,然后利用奇摄动方法构造了问题的形式渐近解,最后利用比较定理,证明了问题广义解的存在性及其渐近性态. 相似文献
18.
Xiaopeng Zhao 《Applicable analysis》2013,92(1):44-59
This article is concerned with a fourth-order parabolic equation. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that the fourth-order parabolic equation possesses a global attractor in H k (0?≤?k?5) space, which attracts any bounded subset of H k (Ω) in the H k -norm. 相似文献
19.
Chuanxi Qian 《Journal of Mathematical Analysis and Applications》2003,284(1):191-205
Consider the third-order nonlinear differential equation
x?+ψ(x,x′)x″+f(x,x′)=p(t), 相似文献