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Luis Escauriaza 《偏微分方程通讯》2013,38(5-6):821-845
It is shown that any elloptic or parabolic operator in nondivergence form with measurable coefficients has a global fundamental solution verifying certain pointwise bounds. 相似文献
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We present the results of an investigation and some applications of fundamental solutions of the Cauchy problem for a new class of parabolic equations. In these equations: (i) there exist three groups of spatial variables, one basic and two auxiliary, (ii) different weights of spatial variables from the basic group with respect to the time variable are admitted, (iii) degeneracies in variables from the auxiliary groups are present, (iv) a degeneracy on the initial hyperplane is present. Pidstryhach Institute of Applied Problems in Mechanics and Mathematics, Ukrainian Academy of Sciences, L'viv; Ternopil' Academy of Economics, Ternopil'. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 41, No. 2, pp. 13–19, April–June, 1998. 相似文献
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Let A be a real symmetric, degenerate elliptic matrix whose degeneracy is controlled by a weight w in the A2 or QC class. We show that there is a heat kernel Wt(x,y) associated to the parabolic equation wut=divA∇u, and Wt satisfies classic Gaussian bounds:
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This paper deals with multivalued identification problems for parabolic equations. The problem consists of recovering a source term from the knowledge of an additional observation of the solution by exploiting some accessible measurements. Semigroup approach and perturbation theory for linear operators are used to treat the solvability in the strong sense of the problem. As an important application we derive the corresponding existence, uniqueness, and continuous dependence results for different degenerate identification problems. Applications to identification problems for the Stokes system, Poisson-heat equation, and Maxwell system are given to illustrate the theory. 相似文献
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《Comptes Rendus Mathematique》2014,352(12):1011-1016
We prove asymptotic convergence results for some analytical expansions of solutions to degenerate PDEs with applications to financial mathematics. In particular, we combine short-time and global-in-space error estimates, previously obtained in the uniformly parabolic case, with some a priori bounds on “short cylinders”, and we achieve short-time asymptotic convergence of the approximate solution in the degenerate parabolic case. 相似文献
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Uniqueness and stability of solution for Cauchy problem of degenerate quasilinear parabolic equations 总被引:2,自引:0,他引:2
ZHAO Junning & ZHAN Huashui Department of Mathematics Xiamen University Xiamen China School of Science Jimei University Xiamen China 《中国科学A辑(英文版)》2005,48(5):583-593
The uniqueness and existence of BV-solutions for Cauchy problem of the form are proved. 相似文献
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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
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Martial Agueh 《Comptes Rendus Mathematique》2003,337(5):331-336
We use mass transportation inequalities to study the asymptotic behavior for a class of doubly degenerate parabolic equations of the form
(1)
where is , or a bounded domain of in which case on . We investigate the case where the potential V is uniformly c-convex, and the degenerate case where V=0. In both cases, we establish an exponential decay in relative entropy and in the c-Wasserstein distance of solutions – or self-similar solutions – of (1) to equilibrium, and we give the explicit rates of convergence. In particular, we generalize to all p>1, the HWI inequalities obtained by Otto and Villani (J. Funct. Anal. 173 (2) (2000) 361–400) when p=2. This class of PDEs includes the Fokker–Planck, the porous medium, fast diffusion and the parabolic p-Laplacian equations. To cite this article: M. Agueh, C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
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On the homogenization of degenerate parabolic equations 总被引:8,自引:0,他引:8
简怀玉 《应用数学学报(英文版)》2000,16(1):100-110
1. Introduction and Main ResultsLet T > 0 and fi C R" be an open bounded domain with Lipschitz boundary. Suppesthat r C on is measurable whose Hausdorff measure H"--'(r) > 0. The outward normito fi is denoted by u = (ul,' ) W). Consider the mixed boundary value problem of thfollowing degenerate parabolic equations of second order:For each s > 0, problem (I.) may be used to describe nonsteady filtration (see [1] and the references therein). The existence, uniquenss and regularity result… 相似文献
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Motivated by a boundary layer problem, we are interested in the controllability properties of parabolic equations degenerating at the boundary of the space domain. We derive new Carleman estimates for a class of degenerate parabolic equation; the proof is based in particular on Hardytype inequalities. Then we deduce observability and null controllability results. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献