Degenerate Integrodifferential Equations Of Parabolic Type With Robin Boundary Conditions: L~2-theory

Angelo Favini; Alfredo Lorenzi; Hiroki Tanabe

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Degenerate Integrodifferential Equations Of Parabolic Type With Robin Boundary Conditions: L~2-theory

机译：具有罗宾边界条件的抛物型退化积分微分方程：L〜2-理论

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This paper is devoted to solving a degenerate parabolic integrod-ifferential equation with the Robin boundary condition. We begin with solving the equation without the integral delay term. For that purpose we introduce some new unknown function following Favini and Yagi [4] and construct the fundamental solution to the equation to be satisfied by it by the method of Kato and Tanabe [5]. Using this fundamental solution we transform the original problem to an easily solvable integral equation for the time derivative of the new unknown function.

机译：本文致力于用罗宾边界条件求解退化的抛物线积分微分方程。我们从没有积分延迟项的方程式开始求解。为此，我们在Favini和Yagi [4]之后引入一些新的未知函数，并通过Kato和Tanabe [5]的方法构造要满足的方程的基本解。使用这个基本解决方案，我们可以将原始问题转换为新未知函数的时间导数的易于求解的积分方程。

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来源
《Journal of the Mathematical Society of Japan》 |2009年第1期|133-176|共44页
作者
Angelo Favini; Alfredo Lorenzi; Hiroki Tanabe;
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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
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关键词
degenerate integrodifferential parabolic equations; robin boundary conditions; multivalued operators; analytic semigroups; fundamental solutions;

机译：退化积分微分抛物方程;罗宾边界条件;多值算子;解析半群;基本解;

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1. ALTERNATING BOUNDARY LAYER TYPE SOLUTIONS OF SOMESINGULARLY PERTURBED PERIODIC PARABOLIC EQUATIONS WITH DIRICHLET AND ROBIN BOUNDARY CONDITIONS [J] . A.B.Vasileva, L.V.Kalachev Журнал вычислительной математики и математической физики . 2007,第2期

机译：具有Dirichlet和Robin边界条件的周期奇异摄动周期抛物型方程的交替边界层解。
2. ALTERNATING BOUNDARY LAYER TYPE SOLUTIONS OF SOMESINGULARLY PERTURBED PERIODIC PARABOLIC EQUATIONS WITH DIRICHLET AND ROBIN BOUNDARY CONDITIONS [J] . A.B.Vasileva, L.V.Kalachev Журнал вычислительной математики и математической физики . 2007,第2期

机译：具有Dirichlet和Robin边界条件的各种扰动周期抛物线方程的交替边界层类型解
3. Classical solvability of multidimensional two-phase Stefan problem for degenerate parabolic equations and Schauder's estimates for a degenerate parabolic problem with dynamic boundary conditions [J] . Degtyarev S. P. Nonlinear differential equations and applications: NoDEA . 2015,第2期

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4. Cahn-Hilliard Approach to Some Degenerate Parabolic Equations with Dynamic Boundary Conditions [C] . Takeshi Fukao IFIP TC 7 conference on system modeling and optimization . 2016

机译：具有动态边界条件的退化简并抛物方程的Cahn-Hilliard方法
5. Boundary value problems for degenerate elliptic-parabolic fourth order equations. [D] . Root, Robert Griffith. 1988

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6. Lyapunov-type inequalities for quasilinear elliptic equations with Robin boundary condition [O] . Ülkü Dinlemez Kantar, Tülay Özden -1

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7. Quasilinear parabolic equations with nonlinear Wentzell–Robin type boundary conditions [O] . Warma Mahamadi 2007

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8. Probabilistic Methods for Finite Difference Approximations to Degenerate Elliptic and Parabolic Equations with Neumann and Dirichlet Boundary Conditions [R] . H. J. Kushner 1974

机译：具有Neumann和Dirichlet边界条件的退化椭圆和抛物型方程有限差分逼近的概率方法

Degenerate Integrodifferential Equations Of Parabolic Type With Robin Boundary Conditions: L~2-theory

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