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Guochun Wen 《中国科学A辑(英文版)》1999,42(7):681-690
The initial-irregular oblique derivative boundary value problems for nonlinear and nondivergence parabolic systems of second
order equations in multiply connected domains are dealt with where coefficients of systems of equations are meaurable. The
uniqueness theorem of solutions for the above problems and somea priori estimates of solutions for the problems are given. And by using the above estimates of solutions and the Leray-Schauder theorem,
the existence of solutions of the initial-boundary value problems is proved. The results are generalizations of corresponding
theorems in literature.
Project supported by the National Natural Science Foundation of China (Grant No. 19671006). 相似文献
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M.V. Safonov 《偏微分方程通讯》2013,38(7-8):1349-1367
A calculus of polyhomogeneous paired Lagrangian distributions, associated to any two cleanly intersecting Lagrangain submanifolds, is constructed. The class is given an intrinsic characterisation using radial operators and a symbol calculus is developed. A class of pseudo—differential operators with singular symbols is developed within the calculus. This is used to give symbolic constructions of parametrices for operators of real principal type and paired Lagrangian distributions. The calculus is then applied to give a symbolic construction of the forward fundamental solution of the wave operator. 相似文献
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D. K. Palagachev 《偏微分方程通讯》2013,38(5-6):867-903
Abstract We present the precise blow-up scenario for the generalized Camassa–Holm equation. We also prove a blow-up result showing that the equation has smooth solutions in which singularities develop in finite time. 相似文献
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The initial-irregular oblique derivative boundary value problems for linear and nondivergence parabolic complex equations
of second order in multiply connected domains are dealt with, where the coefficients of equations are measurable. Firstly
the uniqueness of solutions for the above problems is introduced, and then somea priori estimates of solutions for the problems are given. By using the above estimates and the Leray-Schauder theorem, the existence
of solutions of the initial-boundary value problems can be proved. The results are generalizations of corresponding theorems
in literature.
Project supported by the National Natural Science Foundation of China (Grant No. 19671006). 相似文献
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N. N. Ural'tseva 《Journal of Mathematical Sciences》1994,70(3):1817-1827
A prioriC
2+ estimates are established for the solutions of a fully nonlinear second-order parabolic equation, satisfying a nondegenerate, nonlinear, first-order boundary condition.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademiya Nauk SSSR, Vol. 188, pp. 143–158, 1991. 相似文献
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WEN Guo-chun 《高校应用数学学报(英文版)》2013,28(2):127-137
In this article,we discuss that an oblique derivative boundary value problem for nonlinear uniformly elliptic complex equation of second order with the boundary conditions in a multiply connected unbounded domain D.The above boundary value problem will be called Problem P.Under certain conditions,by using the priori estimates of solutions and Leray-Schauder fixed point theorem,we can obtain some results of the solvability for the above boundary value problem(0.1) and(0.2). 相似文献
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Guochun Wen 《Communications in Nonlinear Science & Numerical Simulation》2000,5(4):174-178
In this paper the initial-irregular oblique derivative problems for fully nonlinear parabolic equations of second order are proposed, and then some a priori estimates of solutions for the above problems are given. 相似文献
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Sungwon Cho 《Journal of Differential Equations》2010,248(4):820-836
We evaluate the rate of decay for solutions to second order parabolic equations, which vanish on the boundary, while the right-hand side is allowed to be unbounded. Our approach is based on a special growth lemma, and it works for both divergence and non-divergence equations, in domains satisfying a general “exterior measure condition” (A). The result for elliptic case is published in Cho and Safonov (2007) [2]. 相似文献
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Guochun Wen 《中国科学A辑(英文版)》1998,41(4):346-356
Oblique derivative boundary value problems for the linear mixed (elliptic-hyperbolic) equation of the second order, i.e. the
generalized Lavrent’ev-Bitsadze equation with weak conditions are discussed. The representation of solutions for the above
boundary value problem is given, the uniqueness and existence of solutions of the above problem are proved, and a priori estimates
of the solutions of the above problem are obtained.
Project supported by the National Natural Science Foundation of China. 相似文献
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A. V. Pokrovskii 《Functional Analysis and Its Applications》2008,42(2):116-125
Let L be a uniformly elliptic linear second order differential operator in divergence form with bounded measurable real coefficients in a bounded domain G ? ?n (n ? 2). We define classes of continuous functions in G that contain generalized solutions of the equation L? = 0 and have the property that the compact sets removable for such solutions in these classes can be completely described in terms of Hausdorff measures. 相似文献
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Journal of Fourier Analysis and Applications - 相似文献
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A. S. Shvedov 《Mathematical Notes》1996,60(5):562-568
The difference schemes of Richardson [1] and of Crank-Nicolson [2] are schemes providing second-order approximation. Richardson's three-time-level difference scheme is explicit but unstable and the Crank-Nicolson two-time-level difference scheme is stable but implicit. Explicit numerical methods are preferable for parallel computations. In this paper, an explicit three-time-level difference scheme of the second order of accuracy is constructed for parabolic equations by combining Richardson's scheme with that of Crank-Nicolson. Restrictions on the time step required for the stability of the proposed difference scheme are similar to those that are necessary for the stability of the two-time-level explicit difference scheme, but the former are slightly less onerous.Translated fromMatematicheskie Zametki, Vol. 60, No. 5, pp. 751–759, November, 1996.This research was supported by the Russian Foundation for Basic Research under grant No. 95-01-00489 and by the International Science Foundation under grants No. N8Q300 and No. JBR100. 相似文献
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We consider a control system for a parabolic equation in a Banach space with uniformly bounded nonlinear termF,
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