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7 papers · 2 filters
Optimal bounds for Neumann eigenvalues in terms of the diameter
Antoine Henrot, Marco Michetti
In this paper, we obtain optimal upper bounds for all the Neumann eigenvalues in two situations (that are closely related). First we consider a one-dimensional Sturm-Liouville eige…
An isoperimetric problem with two distinct solutions
Antoine Henrot, Antoine Lemenant, Ilaria Lucardesi
In this paper we prove that among all convex domains of the plane with two axis of symmetry, the maximizer of the first non trivial Neumann eigenvalue with perimeter constrai…
Shape sensitivity of a 2D Fluid-Structure Interaction problem between a viscous incompressible fluid and an incompressible elastic structure
V. Calisti, I. Lucardesi, J. -F. Scheid
We study the shape differentiability of a general functional depending on the solution of a bidimensional stationary Stokes-Elasticity system, with respect to the reference domain…
Terrace solutions for non-Lipschitz multistable nonlinearities
Thomas Giletti, Ho-Youn Kim, Yong-Jung Kim
Traveling wave solutions of reaction-diffusion equations are well-studied for Lipschitz continuous monostable and bistable reaction functions. These special solutions play a key ro…
Convergence to a terrace solution in multistable reaction-diffusion equations with discontinuities
Thomas Giletti, Ho-Youn Kim
In this paper we address the large-time behavior of solutions of bistable and multistable reaction-diffusion equations with discontinuities around the stable steady states. We show…
Rebuttal to "Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation"
Fatiha Alabau-Boussouira
A paper, entitled "Well-posedness and optimal decay rates for the viscoelastic Kirchhoff equation" was published in 2016, in the journal Boletim da Sociedade Paranaense de Matemati…