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

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