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Ritz-Galerkin method for solving a parabolic equation with non-local and time-dependent boundary conditions

机译:Ritz-Galerkin方法求解具有非局部和时变边界条件的抛物线方程

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摘要

The paper is devoted to the investigation of a parabolic partial differential equation with non-local and time-dependent boundary conditions arising from ductal carcinoma in situ model. Approximation solution of the present problem is implemented by the Ritz-Galerkin method, which is a first attempt at tackling parabolic equation with such non-classical boundary conditions. In the process of dealing with the difficulty caused by integral term in non-local boundary condition, we use a trick of introducing the transition function G(x,t) to convert non-local boundary to another non-classical boundary, which can be handled with the Ritz-Galerkin method. Illustrative examples are included to demonstrate the validity and applicability of the technique in this paper. Copyright (c) 2015 John Wiley & Sons, Ltd.
机译:本文致力于研究由导管癌原位模型引起的具有非局部和时变边界条件的抛物线偏微分方程。本问题的近似解是通过Ritz-Galerkin方法实现的,这是用这种非经典边界条件处理抛物线方程的首次尝试。在处理非局部边界条件下积分项引起的困难的过程中,我们采用了一种技巧,即引入转移函数G(x,t)将非局部边界转换为另一个非经典边界,可以用Ritz-Galerkin方法处理。包括说明性的例子,以证明该技术的有效性和适用性。版权所有(c)2015 John Wiley&Sons,Ltd.

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