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Asymptotic behaviour for a parabolic system with nonlinear boundary conditions.

Julián Fernández Bonder; Julio D. Rossi — 2000

Collectanea Mathematica

A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.

Julián Fernández Bonder; Julio D. Rossi — 2002

Publicacions Matemàtiques

In this paper we study the Sobolev trace embedding W(Ω) → L (∂Ω), where V is an indefinite weight. This embedding leads to a nonlinear eigenvalue problem where the eigenvalue appears at the (nonlinear) boundary condition. We prove that there exists a sequence of variational eigenvalues λ / +∞ and then show that the first eigenvalue is isolated, simple and monotone with respect to the weight. Then we prove a nonexistence result related to the first eigenvalue and we end this article...

Simultaneous vs. non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions

Gabriel Acosta; Julián Fernández Bonder; Pablo Groisman; Julio Daniel Rossi — 2002

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We study the asymptotic behavior of a semi-discrete numerical approximation for a pair of heat equations $u_{t} = Δ u$ , $v_{t} = Δ v$ in $Ω \times (0, T)$ ; fully coupled by the boundary conditions $\frac{\partial u}{\partial η} = u^{p_{11}} v^{p_{12}}$ , $\frac{\partial v}{\partial η} = u^{p_{21}} v^{p_{22}}$ on $\partial Ω \times (0, T)$ , where $Ω$ is a bounded smooth domain in $ℝ^{d}$ . We focus in the existence or not of non-simultaneous blow-up for a semi-discrete approximation $(U, V)$ . We prove that if $U$ blows up in finite time then $V$ can fail to blow up if and only if $p_{11} > 1$ and $p_{21} < 2 (p_{11} - 1)$ , which is the same condition as the one for non-simultaneous blow-up in the continuous problem. Moreover,...

Symmetry properties for the extremals of the Sobolev trace embedding

Julian Fernández Bonder; Enrique Lami Dozo; Julio D. Rossi — 2004

Annales de l'I.H.P. Analyse non linéaire

Simultaneous non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions

Gabriel Acosta; Julián Fernández Bonder; Pablo Groisman; Julio Daniel Rossi — 2010

ESAIM: Mathematical Modelling and Numerical Analysis

We study the asymptotic behavior of a semi-discrete numerical approximation for a pair of heat equations , in Ω x (0,); fully coupled by the boundary conditions $\frac{\partial u}{\partial η} = u^{p_{11}} v^{p_{12}}$ , $\frac{\partial v}{\partial η} = u^{p_{21}} v^{p_{22}}$ on ∂Ω x (0,), where is a bounded smooth domain in $ℝ^{d}$ . We focus in the existence or not of non-simultaneous blow-up for a semi-discrete approximation . We prove that if blows up in finite time then can fail to blow up if and only if > 1 and < 2( - 1) , which is the same...

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Currently displaying 1 – 10 of 10

Asymptotic behaviour for a parabolic system with nonlinear boundary conditions.

A nonlinear eigenvalue problem with indefinite weights related to the Sobolev trace embedding.

Simultaneous vs. non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions

Symmetry properties for the extremals of the Sobolev trace embedding

Simultaneous non-simultaneous blow-up in numerical approximations of a parabolic system with non-linear boundary conditions

Multiple solutions for the $p$ -Laplace equation with nonlinear boundary conditions.

Multiple positive solutions for quasilinear elliptic problems with sign-changing nonlinearities.

Concentration-compactness principle for variable exponent spaces and applications.

Infinitely many solutions for an elliptic system with nonlinear boundary conditions.

Existence results for Hamiltonian elliptic systems with nonlinear boundary conditions.