Biblioteca de la Universidad Complutense de Madrid

Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a non uniformly Lipschitz deformation

Impacto



Arrieta Algarra, José María y Bruschi, Simone M. (2010) Very rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a non uniformly Lipschitz deformation. Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences, 14 (2). 327-351. ISSN 1531-3492

[img]
Vista previa
PDF
463kB

URL Oficial: http://www.aimsciences.org/journals/home.jsp?journalID=2



Resumen

We continue the analysis started in [3] and announced in [2], studying the behavior of solutions of nonlinear elliptic equations in ε with nonlinear boundary conditions of type , when the boundary of the domain varies very rapidly. We show that if the oscillations are very rapid, in the sense that, roughly speaking, its period is much smaller than its amplitude and the function is of a dissipative type, that is, it satisfies , then the boundary condition in the limit problem is , that is, we obtain a homogeneus Dirichlet boundary condition. We show the convergence of solutions in and norms and the convergence of the eigenvalues and eigenfunctions of the linearizations around the solutions. Moreover, if a solution of the limit problem is hyperbolic (non degenerate) and some extra conditions in are satisfied, then we show that there exists one and only one solution of the perturbed problem nearby.


Tipo de documento:Artículo
Palabras clave:Varying boundary; Oscillations; Nonlinear boundary conditions; Elliptic equations; Oscillating boundary; Homogenization; Convergence; Dynamics; Domain
Materias:Ciencias > Matemáticas > Ecuaciones diferenciales
Código ID:13276
Depositado:14 Sep 2011 07:41
Última Modificación:06 Feb 2014 09:45

Sólo personal del repositorio: página de control del artículo