Elder J. Villamizar-Roa, Carlos Banquet
This article concerns the Cauchy problem associated with the nonlinear fourth-order Schrodinger equation with isotropic and anisotropic mixed dispersion. This model is given by the equation
where A is either the operator (isotropic dispersion) or , (anisotropic dispersion), and are real parameters. We obtain local and global well-posedness results in spaces of initial data with low regularity, based on weak- spaces. Our analysis also includes the biharmonic and anisotropic biharmonic equation ; in this case, we obtain the existence of self-similar solutions because of their scaling invariance property. In a second part, we analyze the convergence of solutions for the nonlinear fourth-order Schrodinger equation
as approaches zero, in the -norm, to the solutions of the corresponding biharmonic equation .
Submitted August 22, 2015. Published January 7, 2016.
Math Subject Classifications: 35Q55, 35A01, 35A02, 35C06.
Key Words: Fourth-order Schrodinger equation; biharmonic equation; local and global solutions.
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| Elder J. Villamizar-Roa |
Universidad Industrial de Santander
Escuela de Matemáticas
A.A. 678, Bucaramanga, Colombia
Carlos Banquet |
Universidad de Córdoba
Departamento de Matemáticas y Estadística
A.A. 354, Montería, Colombia
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