Arnaud Rougirel

ON THE ASYMPTOTIC BEHAVIOUR OF THE SOLUTION OF ELLIPTIC PROBLEMS IN CYLINDRICAL DOMAINS BECOMING UNBOUNDED

We study the asymptotic behavior of the solution of linear and nonlinear elliptic problems in cylindrical domains becoming unbounded in one or several directions. In particular we show that this solution converges in H1 norm toward the solution of problems set on the cross section of the domains.

On the asymptotic behaviour of the eigenmodes for elliptic problems in domains becoming unbounded

The aim of this work is to analyze the asymptotic behaviour of the eigenmodes of some elliptic eigenvalue problems set on domains becoming unbounded in one or several directions. In particular, in the case of a linear elliptic operator in divergence form, we prove that the sequence of the

Remarks on the asymptotic behaviour of the solution to parabolic problems in domains becoming unbounded

k

Sur le comportement asymptotique de la solution de problèmes elliptiques dans des domaines cylindriques tendant vers l'infini

-th eigenvalues convergences to the first eigenvalue of an elliptic problems set on the section of the domain. Moreover, an optimal rate of convergence of this sequence is given.

A result of blowup driven by a nonlocal source term

We study the asymptotic behaviour of the solution to linear parabolic problems with nonhomogeneous boundary conditions in domains becoming unbounded in one or several directions. We show that this solution converges locally in space toward the solution of problems set in a cross section of the domains

Eigenvalues, Eigenfunctions in Domains Becoming Unbounded

We study the asymptotic behaviour of the solution of linear and nonlinear elliptic problems in cylindrical domains becoming unbounded in one or several directions. In particular, we give estimates of the difference between the solution in bounded domains and its limit in terms of the size l of the directions going to infinity.

Local and asymptotic analysis of the flow generated by the Cahn–Hilliard–Gurtin equations

Considering a nonlocal semilinear parabolic problem, we prove the existence of solutions which blow up in finite time. These solutions correspond to large negative initial conditions defined on large domains of the real line. The blowup occurs from the nonlinear and nonlocal source term. In this situation the nonlinear and nonlocal boundary term works against blowup.

On the asymptotic behaviour of the solution of parabolic problems in cylindrical domains of large size in some directions

The aim of this work is to analyze the asymptotic behavior of the eigenmodes of some elliptic eigenvalue problems set on domains becoming unbounded in one or several directions.