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The Laplacian with Robin Boundary Conditions on Arbitrary Domains
Potential Analysis, 2003The authors consider the Laplace operator \(\Delta\) on an open set \(\Omega\) in \(\mathbb{R}^n\) with the Robin boundary condition. They deal with the case of an arbitrary Borel measure \(\mu\) on the boundary \(\partial \Omega\), and show that it is always possible to define a realization \(\Delta_\mu\) of the Laplace operator on \(L^2(\Omega ...
Mahamadi Warma, Wolfgang Arendt
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Maxwell–Stokes system with Robin boundary condition
Calculus of Variations and Partial Differential Equations, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On a quenching problem with the robin boundary condition
Nonlinear Analysis: Theory, Methods & Applications, 1991The third initial-boundary value problem for the semilinear heat equation is considered \[ u_ t-\Delta u=f(u),\quad x\in\Omega,\quad t\in(0,T), \] \[ {\partial u/\partial\nu}+a(x,t)u=0,\quad x\in\partial\Omega,\quad t\in(0,T);\quad u(x,0)=u_ 0(x),\quad x\in\Omega. \] Here \(\Omega\) is a bounded smooth domain in \(\mathbb{R}^ n\) \((n\geq 1)\), \(\nu\)
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Problems with Robin Boundary Conditions
2011In this chapter we consider the third type of fundamental boundary value problems, namely, problems with Robin boundary conditions, where a linear combination of the stresses and displacements is prescribed on \(\partial S\).
Gavin R. Thomson, Christian Constanda
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Second Domain Variation for Problems with Robin Boundary Conditions
Journal of Optimization Theory and Applications, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Catherine Bandle, Alfred Wagner
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SIAM Journal on Applied Dynamical Systems, 2015
A new derivation of Robin boundary conditions and interface jump conditions have been presented for one-dimensional diffusion equations. The Robin boundary condition is characterized by randomly switching between the Dirichlet and Neumann conditions.
James Keener, Sean D. Lawley
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A new derivation of Robin boundary conditions and interface jump conditions have been presented for one-dimensional diffusion equations. The Robin boundary condition is characterized by randomly switching between the Dirichlet and Neumann conditions.
James Keener, Sean D. Lawley
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A Hopf bifurcation with Robin boundary conditions
Journal of Dynamics and Differential Equations, 1994zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ashwin, Peter, Mei, Zhen
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Wentzell-Robin boundary conditions on C[0,1]
Semigroup Forum, 2002The author considers the operator \(A_W\) on \(C([0,1])\) defined by: \[ \begin{cases} {\mathcal D}(A_W): =\biggl\{u\in C^2\bigl( [0,1]\bigr) \mid(au')'(j)+ \beta_j u'(j)+ \gamma_ju(j)=0,\;j=0,1\biggr\}\\ A_Wu:=(au')',\end{cases} \] where \(\beta_j\), \(\gamma_j\) \((j=0,1)\) are arbitrary real numbers and the function \(a\in C^1([0,1])\) satisfies \(a(
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Theory of a curved planar waveguide with Robin boundary conditions
Physical Review E, 2010A model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative (Robin boundary condition) is analyzed theoretically within the framework of the linear Schrödinger equation and is applied to the study of the processes in the bent ...
O, Olendski, L, Mikhailovska
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