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Finite Size Critical Behavior for Dirichlet Boundary Conditions
Zeitschrift f�r Physik B Condensed Matter, 1985The behavior, near the upper critical dimension d = 4, of finite size properties at bulk criticality for n -vector models is shown to depend qualitatively on the type of boundary condition (bc). Contrary to the more complicated behavior which holds for periodic bc's, there exists an e = 4 − d expansion for Dirichlet (or free) bc's with only ...
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Optimality Conditions for State-Constrained Dirichlet Boundary Control Problems
Journal of Optimization Theory and Applications, 1999The system is \[ \begin{aligned}{\partial y(t, x) \over \partial t} &= Ay(t, x) + \Phi(t, x, y(t, x)),\quad (t, x) \in (0, T) \times \Omega, \\ y(0, x) &= y_0(x), \qquad x \in \Omega,\end{aligned} \] \((\Omega\) an \(n\)-dimensional domain with boundary \(\Gamma,\) \(A\) a second order elliptic operator).
Arada, N., Raymond, J.-P.
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Semilinear Hemivariational Inequalities with Dirichlet Boundary Condition
2002The paper studies nonsmooth semilinear elliptic boundary value problems which are expressed in the form of hemivariational inequalities. The approach relies on nonsmooth variational methods using essentially a general unilateral growth condition and a new concept of solution. The known results are recovered without additional assumptions.
Dumitru Motreanu, Zdzisław Naniewicz
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Nonlinear Elliptic Equations with Dirichlet Boundary Conditions
2013This chapter studies nonlinear Dirichlet boundary value problems through various methods such as degree theory, variational methods, lower and upper solutions, Morse theory, and nonlinear operators techniques. The combined application of these methods enables us to handle, under suitable hypotheses, a large variety of cases: sublinear, asymptotically ...
Dumitru Motreanu +2 more
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A Linear Thermoelastic Plate Equation with Dirichlet Boundary Condition
Mathematical Methods in the Applied Sciences, 1997Summary: We consider an initial-boundary value problem for a linear thermoelastic plate equation and we prove that the energy associated to the system decays exponentially to zero as time goes to infinity.
Muñoz Rivera, Jaime E. +1 more
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Use of Dirichlet boundary conditions for electron-atom scattering
Physical Review A, 1988An R-matrix variational principle is presented in which the value of the function on the boundary surface is specified rather than its slope or logarithmic slope. Such a boundary condition appears to be convenient for treatment of the ionization process because, in principle, a boundary function can be built up by linear combination of inside solutions.
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A planetary boundary for green water
Nature Reviews Earth & Environment, 2022Lan Wang-Erlandsson +2 more
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Weyl, Dirac and high-fold chiral fermions in topological quantum matter
Nature Reviews Materials, 2021M Zahid Hasan +2 more
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Nonequilibrium boundary-driven quantum systems: Models, methods, and properties
Reviews of Modern Physics, 2022Gabriel T Landi +2 more
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