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.
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页码：65 / 90
页数：26
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