共查询到19条相似文献,搜索用时 78 毫秒
1.
Hongjun YUAN 《数学年刊B辑(英文版)》2007,28(4):475-498
The aim of this paper is to study the continuity of weak solutions for quasilinear degenerate parabolic equations of the form U_t-Δφ(u)=O, whereφ■C~1(R~1)is a strictly monotone increasing function.Clearly,the above equation has strong degeneracy,i.e.,the set of zero points ofφ′(·)is permitted to have zero measure. This is an answer to an open problem in[13,p.288]. 相似文献
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Xu-Jia WANG 《数学年刊B辑(英文版)》2006,27(6):637-642
In this note the author gives an elementary and simple proof for the Schauder estimates for elliptic and parabolic equations. The proof also applies to nonlinear equations. 相似文献
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In this paper we discuss the quasilinear parabolic equationU_■=▽(u~u(1-u)~β.Vu)+■(x,t.u)▽u+C(x,t,u)which is degenerate at u =0 and u=1.Let u(x,t)be a weak solution of the equation satisfying0相似文献
4.
Doklady Mathematics - We consider a quasilinear parabolic boundary value problem with a nonlocal boundary condition of Bitsadze–Samarskii type. A theorem on the existence and uniqueness of a... 相似文献
5.
Feng Ping YAO Yong Yong CAI 《数学学报(英文版)》2007,23(12):2225-2234
The authors present a new proof of L^q interior estimates of the gradient for weak solutions of a quasilinear elliptic equation of p-Laplacian type. 相似文献
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Xiu Hui YANG Fu Cai LI Chun Hong XIE 《数学学报(英文版)》2005,21(4):923-928
Abstract In this paper, we investigate the positive solutions of strongly coupled nonlinear parabolic systems with nonlinear boundary conditions: {ut-a(u, v)△u=g(u, v), vt-b(u, v)△v=h(u, v), δu/δη=d(u, v), δu/δη=f(u, v).Under appropriate hypotheses on the functions a, b, g, h, d and f, we obtain that the solutions may exist globally or blow up in finite time by utilizing upper and lower solution techniques. 相似文献
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In this article we extend ours framework of long-time convergence for numeracal approximations of semihnear parabolic equations prorided in “Wu Haijun and Li Ronghua, Northeast. Math. J. , 16( 1 )(2000), 1-28“, to the Gauss-Ledendre full discretization. When apply the result to the CrankNicholson finiteelement full discretization of the Navier-Stokes equations, we can remore the grid-ratio restriction of “Heywood, J. G. and Rannaeher, R., SIAM J. Numer. Anal., 27(1990), 353-384“,and weaken the stability condition on the continuous solution. 相似文献
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The continuous dependence of bounded Φ-variation solutions on parameters for Kurzweil equations are established by using the functions of bounded Φ-variation that were introduced by Musielak-Orlice. These results are essential generalizations of continuous dependence of bounded variation solutions on parameters for Kurzweil equations. 相似文献
11.
Extinction of Weak Solutions for Nonlinear Parabolic Equations with Nonstandard Growth Conditions 下载免费PDF全文
Jinglu Gao & Bin Guo 《数学研究通讯:英文版》2012,28(4):376-382
This paper deals with the extinction of weak solutions of the initial and
boundary value problem for $u_t$ = div$((|u|^σ + d_0)|∇u|^{p(x)−2}∇u)$. When the exponent
belongs to different intervals, the solution has different singularity (vanishing in finite
time). 相似文献
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Nikolai Dokuchaev 《随机分析与应用》2013,31(3):562-576
Abstract We study linear stochastic partial differential equations of parabolic type with special boundary conditions in time. The standard Cauchy condition at the initial time is replaced by a condition that mixes the values of the solution at different times, including the terminal time and continuously distributed times. Uniqueness, solvability and regularity results for the solutions are obtained. 相似文献
14.
The authors prove a new Carleman estimate for general linear second order parabolic equation with nonhomogeneous boundary conditions. On the basis of this estimate, improved Carleman estimates for the Stokes system and for a system of parabolic equations with a penalty term are obtained. This system can be viewed as an approximation of the Stokes system. 相似文献
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Gui-Qiang G.CHEN 《数学年刊B辑(英文版)》2015,36(5):715-736
This paper presents several examples of fundamental problems
involving weak continuity and compactness for nonlinear partial
differential equations, in which compensated compactness and related
ideas have played a significant role. The compactness and
convergence of vanishing viscosity solutions for nonlinear
hyperbolic conservation laws are first analyzed, including the
inviscid limit from the Navier-Stokes equations to the Euler
equations for homentropic flow, the vanishing viscosity method to
construct the global spherically symmetric solutions to the
multidimensional compressible Euler equations, and the
sonic-subsonic limit of solutions of the full Euler equations for
multi-dimensional steady compressible fluids. Then the weak
continuity and rigidity of the Gauss-Codazzi-Ricci system and
corresponding isometric embeddings in differential geometry are
revealed. Further references are also provided for some recent
developments on the weak continuity and compactness for nonlinear
partial differential equations. 相似文献
17.
Albert Milani 《Mathematische Nachrichten》1999,199(1):115-144
We prove that C2+α,1+α/2 (Q?) solutions of problem (1.6) below are in a subspace Hcm+2(Q) of Hm+2,(m+2)/2(Q) for all m ∈ ?, if f and the coefficients are in Hcm(Q)∪Cα,α/2 (Q?). We apply this result to obtain global existence of Sobolev solutions to the quasilinear problem (1.26) below. 相似文献
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We consider an optimal control problem with indefinite cost for an abstract model, which covers, in particular, parabolic systems in a general bounded domain. Necessary and sufficient conditions are given for the synthesis of the optimal control, which is given in terms of the Riccati operator arising from a nonstandard Riccati equation. The theory extends also a finite-dimensional frequency theorem to the infinite-dimensional setting. Applications include the heat equation with Dirichlet and Neumann controls, as well as the strongly damped Euler–Bernoulli and Kirchhoff equations with the control in various boundary conditions. 相似文献