Parabolic equations with dynamical boundary conditions and source terms on interfaces

DOI10.1007/s10231-013-0329-7zbMath1317.35104arXiv1206.0600OpenAlexW2094003535MaRDI QIDQ466943

A. F. M. ter Elst, Martin Meyries, Joachim Rehberg

Publication date: 31 October 2014

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.0600

zbMATH Keywords

parabolic equation\(L^p\)-regularitymaximal regularitymixed boundary conditiondynamical boundary conditionnonsmooth coefficientsnonsmooth geometryquasilinear parabolic problem

Mathematics Subject Classification ID

Initial-boundary value problems for second-order parabolic equations (35K20) PDEs with low regular coefficients and/or low regular data (35R05) Initial-boundary value problems for PDEs of mixed type (35M13) Quasilinear parabolic equations (35K59)

Related Items (15)

Null controllability for parabolic equations with dynamic boundary conditions ⋮ Well-posedness and exponential stability of boundary control systems with dynamic boundary conditions ⋮ Transmission problems with nonlocal boundary conditions and rough dynamic interfaces ⋮ Parabolic equations with dynamic boundary conditions and drift terms ⋮ Solvability of the heat equation on a half-space with a dynamical boundary condition and unbounded initial data ⋮ Linear and quasilinear evolution equations in the context of weighted \(L_p\)-spaces ⋮ Discrete Carleman estimates and application to controllability for a fully-discrete parabolic operator with dynamic boundary conditions ⋮ Boundary null controllability for the heat equation with dynamic boundary conditions ⋮ The large diffusion limit for the heat equation with a dynamical boundary condition ⋮ The full Keller–Segel model is well-posed on nonsmooth domains ⋮ On maximal parabolic regularity for non-autonomous parabolic operators ⋮ Unnamed Item ⋮ On the numerical range of second-order elliptic operators with mixed boundary conditions in \(L^p\) ⋮ Null controllability for a heat equation with dynamic boundary conditions and drift terms ⋮ A unified framework for parabolic equations with mixed boundary conditions and diffusion on interfaces

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