Gilles Lebeau (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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We prove an observability estimate for a wave equation with rapidly oscillating density, in a bounded domain with Dirichlet boundary condition.
Jianwei Yang (2011)
Applicationes Mathematicae
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We study the initial-boundary problem for a nonlinear system of wave equations with Hamilton structure under Dirichlet's condition. We use the local-in-time Strichartz estimates from [Burq et al., J. Amer. Math. Soc. 21 (2008), 831-845], Morawetz-Pohožaev's identity derived in [Miao and Zhu, Nonlinear Anal. 67 (2007), 3136-3151], and an a priori estimate of the solutions restricted to the boundary to show the existence of global and unique solutions.
Robert Altmann (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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This paper develops a framework to include Dirichlet boundary conditions on a subset of the boundary which depends on time. In this model, the boundary conditions are weakly enforced with the help of a Lagrange multiplier method. In order to avoid that the ansatz space of the Lagrange multiplier depends on time, a bi-Lipschitz transformation, which maps a fixed interval onto the Dirichlet boundary, is introduced. An inf-sup condition as well as existence results are presented for a class...
John W. Barrett, R.M. Shanahan (1990)
Numerische Mathematik
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Aldashev, Serik A. (2010)
Mathematical Problems in Engineering
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I. Babuska, Manil Suri (1987)
Numerische Mathematik
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Matthew D. Blair, Hart F. Smith, Christopher D. Sogge (2009)
Annales de l'I.H.P. Analyse non linéaire
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John W. Barrett, Charles M. Elliott (1986)
Numerische Mathematik
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Dagmar Medková (2008)
Applicationes Mathematicae
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The Dirichlet problem for the Laplace equation for a planar domain with piecewise-smooth boundary is studied using the indirect integral equation method. The domain is bounded or unbounded. It is not supposed that the boundary is connected. The boundary conditions are continuous or p-integrable functions. It is proved that a solution of the corresponding integral equation can be obtained using the successive approximation method.
Ali I. Abdul-Latif (1978)
Collectanea Mathematica
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A. Mouze (2007)
Annales Polonici Mathematici
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We study universal Dirichlet series with respect to overconvergence, which are absolutely convergent in the right half of the complex plane. In particular we obtain estimates on the growth of their coefficients. We can then compare several classes of universal Dirichlet series.