Electron. J. Diff. Eqns., Vol. 2006(2006), No. 89, pp. 1-16.

Nonlinear pseudodifferential equations on a half-line with large initial data

Rosa E. Cardiel, Elena I. Kaikina

Abstract:
We study the initial-boundary value problem for nonlinear pseudodifferential equations, on a half-line,
$$\displaylines{ u_{t}+\mathcal{\lambda}| u| ^{\sigma}u+\mathcal{L} u=0,\quad(x,t)\in{\mathbb{R}^{+}}\times{\mathbb{R}^{+}},\cr u(x,0)=u_{0}(x),\quad x\in{\mathbb{R}}^{+}, }$$
where $\lambda>0$ and pseudodifferential operator $\mathcal{L}$ is defined by the inverse Laplace transform. The aim of this paper is to prove the global existence of solutions and to find the main term of the asymptotic representation in the case of the large initial data.

Submitted February 10, 2006. Published August 9, 2006.
Math Subject Classifications: 35Q35, 35B40.
Key Words: Pseudodifferential operator; large data; asymptotic behavior.

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Rosa E. Cardiel
Instituto de Matemáticas UNAM
(Campus Cuernavaca), Av. Universidad s/n
col. Lomas de Chamilpa, Cuernavaca, Morelos, Mexico
email: rosy@matcuer.unam.mx
Elena I. Kaikina
Instituto de Matemáticas UNAM
Campus Morelia, AP 61-3 (Xangari)
Morelia CP 58089, Michoacán, Mexico
email: ekaikina@matmor.unam.mx

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