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991.
M. Tadi 《Applied mathematics and computation》2010,216(12):3707-3717
This note is concerned with the identification of the unknown diffusion coefficient for a parabolic equation. It introduces an iterative algorithm that can be used to recover the unknown function. The algorithm assumes an initial guess for the unknown function and obtains a background field. It obtains an equation for the error field. It then formulates three forward problems for the error field. These three formulations share the same unknown function which is the correction to the assumed value of the unknown diffusion coefficient. By equating the responses of these three formulations, the algorithm obtains two working equations for the unknown function. A number of numerical examples are also used to study the performance of the algorithm. 相似文献
992.
We present a mass conservative numerical scheme for reactive solute transport in porous media. The transport is modeled by a convection-diffusion-reaction equation, including equilibrium sorption. The scheme is based on the mixed finite element method (MFEM), more precisely the lowest-order Raviart-Thomas elements and one-step Euler implicit. The underlying fluid flow is described by the Richards equation, a possibly degenerate parabolic equation, which is also discretized by MFEM. This work is a continuation of Radu et al. (2008) and Radu et al. (2009) [1] and [2] where the algorithmic aspects of the scheme and the analysis of the discretization method are presented, respectively. Here we consider the Newton method for solving the fully discrete nonlinear systems arising on each time step after discretization. The convergence of the scheme is analyzed. In the case when the solute undergoes equilibrium sorption (of Freundlich type), the problem becomes degenerate and a regularization step is necessary. We derive sufficient conditions for the quadratic convergence of the Newton scheme. 相似文献
993.
A nonlinear iteration method for solving a class of two-dimensional nonlinear coupled systems of parabolic and hyperbolic equations is studied. A simple iterative finite difference scheme is designed; the calculation complexity is reduced by decoupling the nonlinear system, and the precision is assured by timely evaluation updating. A strict theoretical analysis is carried out as regards the convergence and approximation properties of the iterative scheme, and the related stability and approximation properties of the nonlinear fully implicit finite difference (FIFD) scheme. The iterative algorithm has a linear constringent ratio; its solution gives a second-order spatial approximation and first-order temporal approximation to the real solution. The corresponding nonlinear FIFD scheme is stable and gives the same order of approximation. Numerical tests verify the results of the theoretical analysis. The discrete functional analysis and inductive hypothesis reasoning techniques used in this paper are helpful for overcoming difficulties arising from the nonlinearity and coupling and lead to a related theoretical analysis for nonlinear FI schemes. 相似文献
994.
In this paper, the authors establish the regularity in generalized Morrey spaces of solutions to parabolic equations with VMO coefficients by means of the theory of singular integrals and linear commutators. 相似文献
995.
We consider the heat operator acting on differential forms on spaces with complete and incomplete edge metrics. In the latter case we study the heat operator of the Hodge Laplacian with algebraic boundary conditions at the edge singularity. We establish the mapping properties of the heat operator, recovering and extending the classical results from smooth manifolds and conical spaces. The estimates, together with strong continuity of the heat operator, yield short‐time existence of solutions to certain semilinear parabolic equations. Our discussion reviews and generalizes earlier work by Jeffres and Loya. 相似文献
996.
We study the problem of identifying unknown source terms in an inverse parabolic problem, when the overspecified (measured) data are given in form of Dirichlet boundary condition u(0,t) = h(t) and , where is an arbitrarily prescribed subregion. The main goal here is to show that the gradient of cost functional can be expressed via the solutions of the direct and corresponding adjoint problems. We prove Hölder continuity of the cost functional and derive the Lipschitz constant in the explicit form via the given data. On the basis of the obtained results, we propose a monotone iteration process. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
997.
Peng Luo 《Mathematical Methods in the Applied Sciences》2015,38(12):2636-2641
By the means of a differential inequality technique, we obtain a lower bound for blow‐up time if p and the initial value satisfy some conditions. Also, we establish a blow‐up criterion and an upper bound for blow‐up time under some conditions as well as a nonblow‐up and exponential decay under some other conditions. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
998.
R. S. Kraußhar M. M. Rodrigues N. Vieira 《Mathematical Methods in the Applied Sciences》2015,38(18):5305-5319
G. R. Franssens In this paper, we present an explicit construction for the fundamental solution of the heat operator, the Schrödinger operator, and related first‐order parabolic Dirac operators on a class of some conformally flat non‐orientable orbifolds. More concretely, we treat a class of projective cylinders and tori where we can study parabolic monogenic sections with values in different pin bundles. We present integral representation formulas together with some elementary tools of harmonic analysis that enable us to solve boundary value problems on these orbifolds. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
999.
The Crank–Nicolson–Galerkin finite element method for a nonlocal parabolic equation with moving boundaries 下载免费PDF全文
Rui M. P. Almeida José C. M. Duque Jorge Ferreira Rui J. Robalo 《Numerical Methods for Partial Differential Equations》2015,31(5):1515-1533
The aim of this article is to establish the convergence and error bounds for the fully discrete solutions of a class of nonlinear equations of reaction–diffusion nonlocal type with moving boundaries, using a linearized Crank–Nicolson–Galerkin finite element method with polynomial approximations of any degree. A coordinate transformation which fixes the boundaries is used. Some numerical tests to compare our Matlab code with some existing moving finite element methods are investigated. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1515–1533, 2015 相似文献
1000.
Falei WANG 《数学年刊B辑(英文版)》2015,36(4):625-644
This paper deals with backward stochastic differential equations with jumps,
whose data (the terminal condition and coefficient) are given functions of jump-diffusion
process paths. The author introduces a type of nonlinear path-dependent parabolic integrodifferential
equations, and then obtains a new type of nonlinear Feynman-Kac formula
related to such BSDEs with jumps under some regularity conditions. 相似文献