共查询到20条相似文献,搜索用时 15 毫秒
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D. Nomirovskii 《Journal of Differential Equations》2007,233(1):1-21
We consider the following linear parabolic system in a domain with a thin low-permeable insertion (“imperfect interface”):
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We consider the nonlinear parabolic partial differential equations. We construct a discontinuous Galerkin approximation using a penalty term and obtain an optimal L∞(L2) error estimate. 相似文献
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We analyse here a semilinear stochastic partial differential equation of parabolic type where the diffusion vector fields
are depending on both the unknown function and its gradient ∂
xu with respect to the state variable, ∈ ℝn. A local solution is constructed by reducing the original equation to a nonlinear parabolic one without stochastic perturbations
and it is based on a finite dimensional Lie algebra generated by the given diffusion vector fields. 相似文献
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Phan Thanh Nam 《Journal of Mathematical Analysis and Applications》2010,367(2):337-349
We consider the backward parabolic equation
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Lunji Song 《Numerical Methods for Partial Differential Equations》2012,28(1):288-311
In this article, we investigate interior penalty discontinuous Galerkin (IPDG) methods for solving a class of two‐dimensional nonlinear parabolic equations. For semi‐discrete IPDG schemes on a quasi‐uniform family of meshes, we obtain a priori bounds on solutions measured in the L2 norm and in the broken Sobolev norm. The fully discrete IPDG schemes considered are based on the approximation by forward Euler difference in time and broken Sobolev space. Under a restriction related to the mesh size and time step, an hp ‐version of an a priori l∞(L2) and l2(H1) error estimate is derived and numerical experiments are presented.© 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 288–311, 2012 相似文献
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V. V. Skopetskii V. S. Deineka A. L. Artemenko 《Journal of Mathematical Sciences》1994,69(6):1430-1436
Convergence of the approximate solution is proved. Numerical solutions of some examples are given.Kiev University. Translated from Vychislitel'naya i Prikladnaya Matematika, No. 68, pp. 77–85, 1989. 相似文献
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The numerical solution of a parabolic equation with memory is considered. The equation is first discretized in time by means of the discontinuous Galerkin method with piecewise constant or piecewise linear approximating functions. The analysis presented allows variable time steps which, as will be shown, can then efficiently be selected to match singularities in the solution induced by singularities in the kernel of the memory term or by nonsmooth initial data. The combination with finite element discretization in space is also studied.
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D. V. Portnyagin 《Differential Equations》2011,47(4):593-598
We study the complete regularity of solutions of a nondiagonal parabolic system of quasilinear second-order differential equations
in divergence form assuming that the coefficients are sufficiently slowly varying functions of their arguments and the off-diagonal
terms in the coefficient matrix are sufficiently small. To this end, we use a method based on the successive approximation
to the solution by smooth functions with the use of Schauder estimates at each step. 相似文献
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We prove uniqueness of the good solution to the Cauchy–Dirichlet (C–D) problem for linear non-variational parabolic equations
with the coefficients of the principal part with discountinuities, in cases in which in general uniqueness of strong solutions
in Sobolev spaces does not hold. In particular, we prove uniqueness when the discontinuities of the coefficients are contained
in a hyperplane t = t
0 and, with an extra condition on the eigenvalues of the matrix, in a line segment x = x
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Mathematics Subject Classification. 35A05, 35K10, 35K20
Dedicated to the memory of Gene Fabes. 相似文献
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We prove uniqueness of numerical solutions to nonlinear parabolic equations approximated by a fully implicit interior penalty discontinuous Galerkin (IPDG) method, with a mesh-independent constraint on time step. 相似文献
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G. N. Milstein 《Numerical Methods for Partial Differential Equations》2002,18(4):490-522
A number of new layer methods for solving semilinear parabolic equations and reaction‐diffusion systems is derived by using probabilistic representations of their solutions. These methods exploit the ideas of weak sense numerical integration of stochastic differential equations. In spite of the probabilistic nature these methods are nevertheless deterministic. A convergence theorem is proved. Some numerical tests are presented. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 490–522, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/num.10020 相似文献
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Chen Shaohua 《数学学报(英文版)》1994,10(3):325-335
We discuss the existence of global classical solution for the uniformly parabolic equation
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V. V. Skopetskii V. S. Deineka S. G. Shayasyuk 《Journal of Mathematical Sciences》1993,66(4):2381-2387
Finite-element schemes are developed for solving a linear equation of parabolic type with a discontinuous solution in the space variable. Existence and uniqueness of the solution of the corresponding Cauchy problem is proved. Accuracy bounds are obtained for the finite-element scheme and the Crank-Nicholson scheme.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 66, pp. 33–40, 1988. 相似文献
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Lunji Song Gung‐Min Gie Ming‐Cheng Shiue 《Numerical Methods for Partial Differential Equations》2013,29(4):1341-1366
We prove existence and numerical stability of numerical solutions of three fully discrete interior penalty discontinuous Galerkin methods for solving nonlinear parabolic equations. Under some appropriate regularity conditions, we give the l2(H1) and l∞(L2) error estimates of the fully discrete symmetric interior penalty discontinuous Galerkin–scheme with the implicit θ ‐schemes in time, which include backward Euler and Crank–Nicolson finite difference approximations. Our estimates are optimal with respect to the mesh size h. The theoretical results are confirmed by some numerical experiments. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
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Jonathan Zinsl 《Monatshefte für Mathematik》2014,174(4):653-679
We prove global existence of weak solutions of a variant of the parabolic-parabolic Keller–Segel model for chemotaxis on the whole space \({{\mathbb {R}}^d}\) for \(d\ge 3\) with a supercritical porous-medium diffusion exponent and an external drift. The structure of the equations allow the chemotactic drift to be seen both as attraction and repulsion. The method of proof relies on the inherent gradient flow structure of this system with respect to a coupled Wasserstein- \(L^2\) metric. Additional regularity estimates are derived from the dissipation of an entropy functional. 相似文献
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