Global behavior for Whitham type equations on a finite interval |
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| Authors: | Elena I Kaikina |
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| Institution: | (1) Instituto de Matemáticas, UNAM Campus Morelia, AP 61-3(Xangari), CP 58089, Morelia, Michoacán, Mexico |
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| Abstract: | We study the initial-boundary value problem for nonlinear nonlocal equations on a finite interval ![$$\left\{\begin{array}{ll}u_{t}+\lambda |u|^{\sigma}u+\mathbb {K}u = 0,\quad (x, t) \in (0, a) \times \mathbf {R}^{+},\\ u(x, 0) = u_{0}(x),\quad \quad \quad \quad x \in 0, a],\quad \quad \quad \quad \quad (0.1)\\ u(a, t) = 0, \quad \quad \quad \quad \quad \quad t > 0 \end{array}\right.$$](/content/j61511276410555u/526_2008_158_Article_IEq1.gif) where λ > 0 and pseudodifferential operator  is defined by the inverse Laplace transform. The aim of this paper is to prove the global existence of solutions to the inital-boundary
value problem (0.1) and to find the main term of the asymptotic representation in the case of the large initial data. |
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