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101.
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
102.
Shane Cooper 《Applicable analysis》2013,92(7):1401-1430
A two-phase elastic composite with weakly compressible elastic inclusions is considered. The homogenised two-scale limit problem is found, via a version of the method of two-scale convergence, and analysed. The microscopic part of the two-scale limit is found to solve a Stokes type problem and shown to have no microscopic oscillations when the composite is subjected to body forces that are microscopically irrotational. The composites spectrum is analysed and shown to converge, in an appropriate sense, to the spectrum of the two-scale limit problem. A characterisation of the two-scale limit spectrum is given in terms of the limit macroscopic and microscopic behaviours. 相似文献
103.
In this article, we deal with the global existence and nonexistence of solutions to the non-Newtonian polytropic filtration equations coupled with nonlinear boundary conditions. By constructing various kinds of sub- and super-solutions and using the basic properties of M-matrix, we give the necessary and sufficient conditions for global existence of nonnegative solutions. The critical curve of Fujita type is conjectured with the aid of some new results, which extend the recent results of Zheng, Song, and Jiang [Critical Fujita exponents for degenerate parabolic equations coupled via nonlinear boundary flux, J. Math. Anal. Appl. 298 (2004), pp. 308–324], Zhou and Mu [Critical curve for a non-Newtonian polytropic filtration system coupled via nonlinear boundary flux, Nonlinear Anal. 68 (2008), pp. 1–11], and Zhou and Mu [Algebraic criteria for global existence or blow-up for a boundary coupled system of nonlinear diffusion equations, Appl. Anal. 86 (2007), pp. 1185–1197] to more general equations. 相似文献
104.
《Stochastics An International Journal of Probability and Stochastic Processes》2013,85(8):1170-1189
ABSTRACTThe paper studies backward stochastic partial differential equations (BSPDEs) of parabolic type in bounded domains in the setting where the coercivity condition is not necessary satisfied and under special non-local in time and space boundary conditions replacing the standard Cauchy condition. These conditions connect the terminal value of the solution with a functional over the entire past solution. Uniqueness, solvability, and regularity results are obtained. As an example of applications, it is shown that degenerate BSPDEs with non-local boundary conditions arise naturally in modelling of portfolio selection problems, including models where dividend payoffs and management fees are taken into account. 相似文献
105.
Delphine Salort 《偏微分方程通讯》2013,38(2):209-228
We consider some linear Schrödinger equation with variable coefficients associated to a smooth symmetric metric g which can be degenerate, without sign and such that g has a submatrix of fixed rank v which is uniformly nondegenerate. In this general setting we prove Strichartz estimates with a loss of derivative on the solution. We also discuss the problem of the control of high frequencies. In particular, we prove that if the equation preserves the H s norm for all s ≥ 0, then we obtain almost the same Strichartz estimates as those for the Schrödinger equation associated to a Riemannian metric of dimension 2d ? v. 相似文献
106.
In this paper, we consider the Cauchy problem of semi-linear degenerate backward stochastic partial differential equations (BSPDEs) under general settings without technical assumptions on the coefficients. For the solution of semi-linear degenerate BSPDE, we first give a proof for its existence and uniqueness, as well as regularity. Then the connection between semi-linear degenerate BSPDEs and forward–backward stochastic differential equations (FBSDEs) is established, which can be regarded as an extension of the Feynman–Kac formula to the non-Markovian framework. 相似文献
107.
《偏微分方程通讯》2013,38(11-12):1697-1744
Abstract In this paper, we consider the thin film equation u t + div(|u| n ?Δu) = 0 in the multi-dimensional setting and solve the Cauchy problem in the parameter regime n ∈ [2, 3). New interpolation inequalities applied to the energy estimate enable us to control third order derivatives of appropriate powers of solutions. In such a way, a natural solution concept – reminiscent of that one used by Bernis and Friedman [Bernis, F., Friedman, A., (1990). Higher order nonlinear degenerate parabolic equations. J. Differential Equations 83:179–206] in space dimension N = 1 ? becomes available for the first time in the multi-dimensional setting. In addition, we provide the key integral estimate to establish results on the qualitative behavior of solutions like finite speed of propagation or occurrence of a waiting time phenomenon. 相似文献
108.
《偏微分方程通讯》2013,38(11-12):2029-2044
109.
110.