ON THE NUMERICAL SOLUTION OF SEMILINEAR PARABOLIC PROBLEMS IN MULTICOMPONENT STRUCTURES WITH VOLTERRA OPERATORS IN THE TRANSMISSION CONDITIONS AND IN THE BOUNDARY CONDITIONS

Kacur J.; Vankeer R.

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ON THE NUMERICAL SOLUTION OF SEMILINEAR PARABOLIC PROBLEMS IN MULTICOMPONENT STRUCTURES WITH VOLTERRA OPERATORS IN THE TRANSMISSION CONDITIONS AND IN THE BOUNDARY CONDITIONS

机译：透射和边界条件下含Volterra算子的多组分结构半线性抛物线问题的数值解

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This paper deals with a Rothe Galerkin finite element method for a class of parabolic problems in composite media. At the internal boundaries both the conormal derivative (heat flux) and the unknown function (temperature) may be discontinuous. Fairly general jumps are allowed, viz. being expressed in terms of Volterra operators acting on the unknown from both sides of the interfaces. Both the conductivity matrices and the source terms may be dependent on the unknown. Finally also the natural boundary conditions may include Volterra operators. Such imperfect (thermal) contact problems arise e.g. when modelling some heat transfer problems in buildings, see for instance [5] and [10]. [References: 12]

机译：本文针对复合介质中的一类抛物线问题，采用了Rothe Galerkin有限元方法。在内部边界处，正态导数（热通量）和未知函数（温度）可能不连续。相当普遍的跳跃是允许的，即。用Volterra运算符表示，它们从接口的两侧作用于未知数。电导率矩阵和源项都可能取决于未知数。最后，自然边界条件也可以包括Volterra算子。这种不完美的（热）接触问题例如会出现。在对建筑物中的一些传热问题进行建模时，请参见例如[5]和[10]。 [参考：12]

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《Zeitschrift fur Angewandte Mathematik und Mechanik》 |1995年第2期|共13页
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Kacur J.; Vankeer R.;
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1. ON THE NUMERICAL SOLUTION OF SEMILINEAR PARABOLIC PROBLEMS IN MULTICOMPONENT STRUCTURES WITH VOLTERRA OPERATORS IN THE TRANSMISSION CONDITIONS AND IN THE BOUNDARY CONDITIONS [J] . Kacur J., Vankeer R. Zeitschrift fur Angewandte Mathematik und Mechanik . 1995,第2期

机译：透射和边界条件下含Volterra算子的多组分结构半线性抛物线问题的数值解
2. Full discretization of a nonlinear parabolic problem containing volterra operators and an unknown dirichlet boundary condition [J] . Grimmonprez Marijke, Slodicka Marian Numerical Methods for Partial Differential Equations: An International Journal . 2015,第5期

机译：包含Volterra算子和未知Dirichlet边界条件的非线性抛物问题的完全离散化。
3. On Global Existence of Solutions of Initial Boundary Value Problem for a System of Semilinear Parabolic Equations with Nonlinear Nonlocal Neumann Boundary Conditions [J] . Gladkova A. L., Nikitin A. I. Differential equations: A translation of differensial'nye uraveniya . 2018,第1期

机译：非线性非局部Neumann边界条件下半线性抛物线方程系统初值问题解决方案的全局存在
4. Numerical techniques for the recovery of an unknown Dirichlet data function in semilinear parabolic problems with nonstandard boundary conditions [C] . Roger Van Keer, Marian Slodicka International Conference on Numerical Analysis and Its Applications . 2001

机译：非标准边界条件恢复半线性抛物面问题中未知Dirichlet数据函数的数值技术
5. ASYMPTOTIC BEHAVIOR OF RADIAL SOLUTIONS TO AN ELLIPTIC-PARABOLIC SYSTEM WITH NONLINEAR BOUNDARY CONDITIONS [D] . 飯田, 雅人 1995

机译：具有非线性边界条件的椭圆抛物型方程组的径向解的渐近性
6. A Class of Nonlocal Coupled Semilinear Parabolic System with Nonlocal Boundaries [O] . Hong Liu, Haihua Lu -1

机译：一类具有非局部边界的非局部耦合半线性抛物方程组
7. NUMERICAL SOLUTION OF THE BOUNDARY PROBLEM FOR PARABOLIC EQUATION WITH NON-SELF-ADJOINT OPERATOR AND RELATED BOUNDARY CONDITIONS [O] . B. Dovgiy, L. Vakal, E. Vakal 2020

机译：非自伴随算子和相关边界条件的抛物线方程边界问题的数值解
8. A Method for the Numerical Solution of Two-Point Boundary Value Problems Based on the Use of Volterra Integral Operators. [R] . fujita, h. rall, l. b. 1973

机译：基于Volterra积分算子的两点边值问题数值解法。

ON THE NUMERICAL SOLUTION OF SEMILINEAR PARABOLIC PROBLEMS IN MULTICOMPONENT STRUCTURES WITH VOLTERRA OPERATORS IN THE TRANSMISSION CONDITIONS AND IN THE BOUNDARY CONDITIONS

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