CONVERGENCE AND DENSITY RESULTS FOR PARABOLIC QUASI-LINEAR VENTTSEL' PROBLEMS IN FRACTAL DOMAINS

被引：7

作者：

Creo, Simone ^{[1
]}

Durante, Valerio Regis ^{[1
]}

机构：

[1] Univ Roma Sapienza, Dipartimento Sci Base & Appl Ingn, Via A Scarpa 16, I-00161' Rome, Italy

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2019年 / 12卷 / 01期

关键词：

Fractal surfaces; density results; asymptotic behavior; Venttsel' problems; nonlinear energy forms; trace theorems; varying Hilbert spaces; p-Laplacian; nonlinear semigroups; HEAT-FLOW PROBLEMS; DIRICHLET FORMS; SOBOLEV SPACES; APPROXIMATION; BOUNDARY; CURVE;

D O I：

10.3934/dcdss.2019005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a quasi-linear evolution equation with nonlinear dynamical boundary conditions in a three dimensional fractal cylindrical domain Q, whose lateral boundary is a fractal surface S. We consider suitable approximating pre-fractal problems in the corresponding pre-fractal varying domains. After proving existence and uniqueness results via standard semigroup approach, we prove density results for the domains of energy functionals defined on Q and S. Then we prove that the pre-fractal solutions converge in a suitable sense to the limit fractal one via the Mosco convergence of the energy functionals.

引用

页码：65 / 90

页数：26

共 46 条

[41] Quasi-linear variable exponent boundary value problems with Wentzell-Robin and Wentzell boundary conditions [J].

Velez-Santiago, Alejandro .

JOURNAL OF FUNCTIONAL ANALYSIS, 2014, 266 (02) :560-615

[42] A space-time pseudospectral method for solving multi-dimensional quasi-linear parabolic partial differential (Burgers') equations [J].

Mittal, A. K. .

APPLIED NUMERICAL MATHEMATICS, 2024, 195 :39-53

[43] Two-scale convergence of periodic elliptic spectral problems with indefinite density function in perforated domains [J].

Douanla, Hermann .

ASYMPTOTIC ANALYSIS, 2013, 81 (3-4) :251-272

[44] FINITE ELEMENT METHODS FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY LINEAR QUASI-PARABOLIC INTEGRO-DIFFERENTIAL EQUATIONS [J].

Shen, Wanfang ;

Ge, Liang ;

Yang, Danping .

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING, 2013, 10 (03) :536-550

[45] Optimal convergence analysis of a linearized second-order BDF-PPIFE method for semi-linear parabolic interface problems [J].

Yi, Huaming ;

Chen, Yanping ;

Wang, Yang ;

Huang, Yunqing .

APPLIED MATHEMATICS AND COMPUTATION, 2023, 438

[46] High-resolution compact numerical method for the system of 2D quasi-linear elliptic boundary value problems and the solution of normal derivatives on an irrational domain with engineering applications [J].

Priyadarshini, Ishaani ;

Mohanty, R. K. .

ENGINEERING WITH COMPUTERS, 2022, 38 (SUPPL 1) :539-560

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