Weak solutions for a nonlinear dispersive equation |
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Authors: | LA Medeiros MMilla Miranda |
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Institution: | Instituto de Matematica, Universidade Federal do Rio de Janeiro, Caixa Postal 1835-ZC-OO, Rio de Janeiro—RJ, Brazil |
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Abstract: | In this paper we study the existence, uniqueness, and regularity of the solutions for the Cauchy problem for the evolution equation is in (0, 1), 0 ? t ? T, T is an arbitrary positive real number,f(s)?C1, and g(x, t)?L∞(0, T; L2(0, 1)). We prove the existence and uniqueness of the weak solutions for (1) using the Galerkin method and a compactness argument such as that of J. L. Lions. We obtain regular solutions using eigenfunctions of the one-dimensional Laplace operator as a basis in the Galerkin method. |
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