共查询到20条相似文献,搜索用时 187 毫秒
1.
ZHANG Xi-cheng 《数学杂志》2021,(1):1-4
In this note we announce the global boundedness for the solutions to a class of possibly degenerate parabolic equations by De-Giorgi’s iteration.In particular,the existence of weak solutions for possibly degenerate stochastic differential equations with singular diffusion coefficients is obtained. 相似文献
2.
Yongzhong Wang 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(7-8):3289-3302
In this paper, we consider nonnegative weak solutions for a class of degenerate parabolic equations. Using Moser’s method, we get the local boundedness of solutions to equations of this class. Then we prove that the solutions are locally Hölder continuous. 相似文献
3.
In this paper, we discuss the existence of weak solutions to the initial and boundary value problem of a class of nonlinear degenerate parabolic equations in non-divergence form. Applying the method of parabolic regularization, we prove the existence of weak solutions to the problem. By carefully analyzing the approximate solutions to the problem, we make a series of estimates to the solutions and prove the weak convergence of the approximation solution sequence. Finally we testify the existence of weak solutions to the problem. 相似文献
4.
§ 1.Introduction Inthispaperwestudythestrongandweakpropertyoftravellingwavefrontsolutions (TWFS)forthefollowingdegenerateparabolicequation : ψ(u) t = 2 u x2 +f(u) . ( 1 .1 ) Welookforsolutionsof( 1 .1 )oftheformu(x,t) =q(x -ct) (cisthewavespeed) ,whereq( ξ) ,ξ=x -ct,asafunctionofas… 相似文献
5.
Youssef Ouknine 《随机分析与应用》2013,31(4):871-888
Abstract The article is devoted to representation of weak solutions (in Sobolev sense) of degenerate parabolic partial differential equations through forward-backward stochastic differential equations. Before, we prove a weak version of a norm equivalence result. 相似文献
6.
Ming Yu Chen 《数学学报(英文版)》2008,24(9):1525-1532
In this paper, we give a complete picture of the blow-up criteria for weak solutions of the Dirichlet problem of some doubly
degenerate nonlinear parabolic equations.
The project is supported by the Natural Science Foundation of Fujian Province of China (No. Z0511048) 相似文献
7.
Huashui Zhan & Zhaosheng Feng 《分析论及其应用》2022,38(3):297-321
For the nonlinear degenerate parabolic equations, how to find an appropriate boundary value condition to ensure the well-posedness of weak solution has been
an interesting and challenging problem. In this paper, we develop the general characteristic function method to study the stability of weak solutions based on a partial
boundary value condition. 相似文献
8.
We prove the Hölder regularity of bounded weak solutions of doubly nonlinear degenerate parabolic equations with measurable coefficients. 相似文献
9.
Potential Analysis - We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to degenerate parabolic equations of p-laplacian type.... 相似文献
10.
We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in the research of degenerate parabolic equations including porous medium equations. Consequently, we prove that a function in such a class is continuous. As an application, we obtain the estimate for the continuous modulus of the solutions of a few degenerate parabolic equations in divergence form, including the anisotropic porous equations. 相似文献
11.
We study some classes of functions satisfying the assumptions similar to but weaker than those for the classical B2 function classes used in the research of quasi-linear parabolic equations as well as the ones used in the research of degenerate parabolic equations including porous medium equationsl.Comsequently,we prove that a function in such a class is continuous.As an application,we obtain the estimate for the continuous modulus of the solutions of a few degenerate parabolic equations in divergence form,including the anisotropic porous equations. 相似文献
12.
Shulin Zhou 《偏微分方程(英文版)》1994,7(4):289-322
In this paper, the notion named parabolic Q-minima is endowed with rich meanings and its local behavior is investigated. As its direct application we obtain the local regularity, such as boundcdncss, continuity, llolder continuity of the weak solutions of the various filtration equations, e.g., the equation of Newtonian polytropic filtration, the general equation of Newtonian filtration, the equation of elastic filtration, the equation of non-Newtonian polytropic filtration. Therefore, a unifying approach to various regularity results for a great number of nonlinear degenerate parabolic equations is provided. 相似文献
13.
14.
Conditions for the existence and uniqueness of weak solutions for a class of nonlinear nonlocal degenerate parabolic equations are established. The asymptotic behaviour of the solutions as time tends to infinity are also studied. In particular, the finite time extinction and polynomial decay properties are proved. 相似文献
15.
Ning Su 《应用数学学报(英文版)》1990,6(2):135-144
A degenerate parabolic system arising from the fluid-solute-heat flow through unsaturated porous media is considered. The existence of weak solutions to the initial boundary value problem of this system is established by parabolic regularization. The regularity is proved as well, i. e. the weak solutions satisfy the equations and initial boundary conditions pointwise in the region where the moisture content is positive.This project is supported by National Natural Science Foundation of China. 相似文献
16.
Mikko Parviainen 《Annali di Matematica Pura ed Applicata》2009,188(2):333-358
This paper studies the global regularity theory for degenerate nonlinear parabolic partial differential equations. Our objective
is to show that weak solutions belong to a higher Sobolev space than assumed a priori if the complement of the domain satisfies
a capacity density condition and if the boundary values are sufficiently smooth. Moreover, we derive integrability estimates
for the gradient. The results extend to the parabolic systems as well. The higher integrability estimates provide a useful
tool in several applications.
相似文献
17.
This paper deals with a degenerate parabolic system coupled via general reaction terms of power type. Global weak solutions are obtained by means of energy estimates and the De Giorgi's technique. In particular, the criterion for global nonexistence of weak solutions is proved by introducing suitable weak sub-solutions together with a weak comparison principle. In summary, the critical exponent for weak solutions of the degenerate parabolic system is determined. 相似文献
18.
一类双重退化抛物方程局部解的存在性 总被引:1,自引:0,他引:1
This paper deals with a class of doubly degenerate parabolic equations, including as particular cases the porous medium equation and the degenerate p- Laplace equation(p>2) u_t-div(b(x,t,u)|▽u|~(p-2)▽u)=f(x,u,t). The initial-boundary value problem in a bounded domain of R~N is considered under mixed boundary conditions.The existence of local-in-time weak solutions is obtained. 相似文献
19.
Stefano Lisini Daniel Matthes Giuseppe Savaré 《Journal of Differential Equations》2012,253(2):814-850
In this paper, we establish a novel approach to proving existence of non-negative weak solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and certain thin film equations. The considered evolution equations are in the form of a gradient flow for a perturbed Dirichlet energy with respect to a Wasserstein-like transport metric, and weak solutions are obtained as curves of maximal slope. Our main assumption is that the mobility of the particles is a concave function of their spatial density. A qualitative difference of our approach to previous ones is that essential properties of the solution – non-negativity, conservation of the total mass and dissipation of the energy – are automatically guaranteed by the construction from minimizing movements in the energy landscape. 相似文献
20.
渗流方程差分解的收敛性 总被引:1,自引:0,他引:1
渗流方程是拟线性退化抛物型方程。[1—4]讨论了弱解的存在唯一性问题。由于非线性扩散系数有零点,其解可以不光滑。在[5,6]中研究了渗流方程 u_t=(u~m)_(xx),m>1的差分方法问题,对光滑区和弱间断点给以分别处理。渗流方程的解是连续的,但在有些点上导数不存在。因此,不能用Taylor展开估计截断误差的方法证明差分解的收敛性。 相似文献