arXiv subjects

Victor Cañulef-Aguilar

Publications and source records attributed to Victor Cañulef-Aguilar.

4 recordsLinked to original sources

arXiv2022

On the collapse of the local Rayleigh condition and the finite time blow-up for the semi-lagrangian equations

In this paper we study the propagation of the local Rayleigh condition for the two-dimensional hydrostatic Euler equation in the framework of the local well-posedness result by Masmoudi and Wong \cite{MaTKW12}. We show under certain assumptions that such solutions will develop singularities or collapse the local Rayleigh condition. In addition, we find necessary conditions for the global solvability. Finally, we establish the finite time blow-up of solutions to the semi-lagrangian equations introduced by Brenier in \cite{Bre99} for certain class of initial data.

math.AP↗

arXiv2019

A lower bound for the void coalescence load in nonlinearly elastic solids

The problem of the sudden growth and coalescence of voids in elastic media is considered. The Dirichlet energy is minimized among incompressible and invertible Sobolev deformations of a two-dimensional domain having $n$ microvoids of radius $\varepsilon$. The constraint is added that the cavities should reach at least certain minimum areas $v_{1},...,v_{n}$ after the deformation takes place. They can be thought of as the current areas of the cavities during a quasistatic loading, the variational problem being the way to determine the state to be attained by the elastic body in a subsequent time step. It is proved that if each $v_{i}$ is smaller than the area of a disk having a certain well defined radius, which is comparable to the distance, in the reference configuration, to either the boundary of the domain or the nearest cavity (whichever is closer), then there exists a range of external loads for which the cavities opened in the body are circular in the $\varepsilon \rightarrow 0$ limit.

math.AP↗

arXiv2019

Hölder estimates for the Neumann problem in a domain with holes and a relation formula between the Dirichlet and Neumann problems

In this paper we study the dependence of the Hölder estimates on the geometry of a domain with holes for the Neumann problem. For this, we study the Hölder regularity of the solutions to the Dirichlet and Neumann problems in the disk (and in the exterior of the disk), from which we get a relation between harmonic extensions and harmonic functions with prescribed Neumann condition on the boundary of the disk (for both interior and exterior problems).

math.AP↗

arXiv2019

Multiple Independent Cavitation in 2D NeoHookean Materials

In this thesis we find an upper bound for the stretch factor of an elastic incompressible material subject to multiaxial traction, under which one can ensure that there is still no coalescence. The problem involves classical elliptic regularity theory (and the analysis of the dependence of the estimates on the domain), from which we get a regularity result for a free boundary problem.

math.AP↗