The one-dimensional wave equation with general boundary conditions |
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Authors: | Edgardo Alvarez-Pardo Mahamadi Warma |
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Affiliation: | 1.Department of Mathematics, Faculty of Natural Sciences,University of Puerto Rico,San Juan,USA |
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Abstract: | We show that a realization of the Laplace operator Au := u′′ with general nonlocal Robin boundary conditions α j u′(j) + β j u(j) + γ 1–j u(1 ? j) = 0, (j = 0, 1) generates a cosine family on L p (0, 1) for every ({p,{in},[1,infty)}). Here α j , β j and γ j are complex numbers satisfying α 0, α 1 ≠ 0. We also obtain an explicit representation of local solutions to the associated wave equation by using the classical d’Alembert’s formula. |
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