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1.
In this paper, we establish interior Hölder estimates of solutions for double degenerate nonlinear parabolic equations (u^{q-1})_t = div (|∇u|^{p-2}∇u) when 1 < p < 2, p ≤ q. 相似文献
2.
We investigate the unique solvability of second order parabolic equations in non-divergence form in , p ≥ 2. The leading coefficients are only measurable in either one spatial variable or time and one spatial variable. In addition,
they are VMO (vanishing mean oscillation) with respect to the remaining variables.
The second author was partially supported by NSF Grant DMS-0140405. 相似文献
3.
In this paper, we give some regularity results of solutions to nonlinear parabolic equations with a lower-order term and inregular data. 相似文献
4.
Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients
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Hongjie Dong 《分析论及其应用》2020,36(2):161-199
In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations. 相似文献
5.
Interior regularity results for viscosity solutions of fully nonlinear uniformly parabolic equations under the Dini condition,
which improve and generalize a result due to Kovats, are obtained by the use of the approximation lemma.
Received November 21, 2000, Accepted April 27, 2001 相似文献
6.
We obtain a criterion for invertibility in Hölder spaces of linear parabolic operators of arbitrary order with any number of spatial variables and almost-periodic coefficients. 相似文献
7.
带非线性边界条件的非线性抛物型方程组 总被引:1,自引:0,他引:1
本文讨论带非线性边界条件的抛物型方程组ut=Δum,vt=Δvm,x∈Ω,t>0,un=vp,vn=uq,x∈Ω,t>0,u(x,0)=u0(x)δ>0,v(x,0)=v0(x)δ>0,x∈Ω(I)解的整体存在性和在有限时刻爆破问题.其中m,p,q>0,ΩIRN是有界光滑区域,δ>0可以充分小. 相似文献
8.
Bai Donghua 《偏微分方程(英文版)》1992,5(2)
We consider a free boundary problem connected with non-Newtonian fluid motion, i.e. the flow of power law fluids with the yield stress. We obtain the solution of the relevant approximation problem by means of a parabolic quasi-variational inequality, and then obtain the weak solution of the original problem after a passage to the limit. Finally, we study the regularity of the weak solution. 相似文献
9.
Parabolic Capacity and Soft Measures for Nonlinear Equations 总被引:2,自引:0,他引:2
We first introduce, using a functional approach, the notion of capacity related to the parabolic p-Laplace operator. Then we prove a decomposition theorem for measures (in space and time) that do not charge the sets of null capacity. We apply this result to prove existence and uniqueness of renormalized solutions for nonlinear parabolic initial boundary-value problems with such measures as right-hand side. 相似文献
10.
Jessica Lin 《偏微分方程通讯》2015,40(9):1688-1704
This note establishes an interior quantitative lower bound for nonnegative supersolutions of fully nonlinear uniformly parabolic equations. The result may be interpreted as a quantitative version of a growth lemma established by Krylov and Safonov for nonnegative supersolutions of linear uniformly parabolic equations in nondivergence form. Our approach is different, and follows from an application of a reverse Holder inequality. The result is the parabolic analogue of an elliptic regularity estimate established by Caffarelli, Souganidis, and Wang in the stochastic homogenization of fully nonlinear uniformly elliptic equations. 相似文献
11.
An ADI scheme for solving three-dimensional parabolic equations withfirst-order derivatives and variable coefficients has been developed basedon our previous papers and the idea of the modified upwind differencescheme. This ADI scheme is second-order accurate and unconditionallystable. Further, a small parameter can be chosen which makes it suitablefor simulating fast-transient phenomena or for computations on fine spatialmeshes. The method is illustrated with numerical examples. 相似文献
12.
Mirjana STOJANOVIC 《数学学报(英文版)》2006,22(2):393-406
We consider nonlinear parabolic equations with nonlinear non-Lipschitz's term and singular initial data like Dirac measure, its derivatives and powers. We prove existence-uniqueness theorems in Colombeau vector space yC^1,W^2,2([0,T),R^n),n ≤ 3. Due to high singularity in a case of parabolic equation with nonlinear conservative term we employ the regularized derivative for the conservative term, in order to obtain the global existence-uniqueness result in Colombeau vector space yC^1,L^2([0,T),R^n),n≤ 3. 相似文献
13.
建立了一类高阶非线性变系数函数方程一切解振动的几个充分条件,并且给出了在差分方程中的若干应用.结果全面推广了某些文献的结果. 相似文献
14.
LIU Ke-ying XU Shao-xian LIU An-ping 《数学季刊》2005,20(4):342-349
This paper deals with the oscillatory properties of a class of nonlinear neutral parabolic partial differential equations with several delays. Sufficient criteria for the equation to be oscillatory are obtained by making use of some results of first-order functional differential inequalities. These results fully reveal the essential difference between this type and that without delays. 相似文献
15.
Implicit–explicit multistep methods for nonlinear parabolic equations were recently analyzed. If the implicit scheme is one of the backward differentiation formulae (BDF) of order up to six, then the corresponding implicit–explicit method of the same order is stable provided the stability constant is less than a specific scheme-dependent constant. Based on BDF, implicit methods are constructed such that the corresponding implicit–explicit scheme of the same order exhibits improved stability properties. 相似文献
16.
将一个低阶Crouzeix-Raviart型非协调三角形元应用到一类非线性抛物方程,并建立了质量集中的半离散和向后Euler全离散逼近格式,在一般各向异性网格上利用插值算子导出了L2-模的最优误差估计. 相似文献
17.
We address the self-similar solvability of a singular parabolic problem and show that solutions to parabolic fully nonlinear equations are not expected to be C 2,1. 相似文献
18.
Zhou Shulin 《偏微分方程(英文版)》1993,6(3)
In this paper, we have generalized the notion of parabolic Q-minima in [1] to provide a unifying approach to obtain some regulariity results for certain nonlinear degenerate parabolic equations. 相似文献
19.
研究一类具非线性扩散项的脉冲抛物型方程解的强迫振动性问题,借助平均技巧和脉冲微分不等式,建立了该类方程在Dirichlet边值条件下所有解强迫振动的若干新的充分判据.结论充分表明振动是由脉冲效应引起的. 相似文献