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.

Convergence and density results for parabolic quasi-linear Venttsel’ problems in fractal domains / Creo, Simone; Regis Durante, V.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 1:12(2019), pp. 65-90. [10.3934/dcdss.2019005]

Convergence and density results for parabolic quasi-linear Venttsel’ problems in fractal domains

CREO, SIMONE
;
REGIS DURANTE, VALERIO
2019

Abstract

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.
Fractal surfaces, density results, asymptotic behavior, Venttsel' problems, nonlinear energy forms, trace theorems, varying Hilbert spaces, p-Laplacian, nonlinear semigroups.
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Convergence and density results for parabolic quasi-linear Venttsel’ problems in fractal domains / Creo, Simone; Regis Durante, V.. - In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S. - ISSN 1937-1632. - 1:12(2019), pp. 65-90. [10.3934/dcdss.2019005]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1186216
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