CAPDE

“On the non-local Lazer-McKenna conjecture with superlinear potential under a partial symmetry condition on the domain: Critical and supercritical cases”

Event Date: Mar 25, 2019 in CAPDE, Differential Equations, Seminars

Abstract: “In 1983 A. Lazer and P.J. McKenna conjectured that the Ambrosetti-Prodi type problems have an unbounded number of solutions as a defined parameter grows to infinity. There were not results on this conjecture, other than the one dimensional case, until 2003 by Breuer . In this talk we will see the existence of a family of solutions indexed by a real number for the non-local problem with superlinear potential under a partial symmetry condition on the domain”

Read More

Cross-diffusion and entropy in population dynamics

Event Date: Mar 11, 2019 in CAPDE, Seminars

Abstract: In Population dynamics, reaction-cross diffusion systems model the evolution of the populations of competing species with a segregation effect between individuals. For these strongly coupled, often nonlinear systems, a question as basic as the existence of solutions appears to be extremely complex. We introduce an approach based on duality and entropy methods. We prove the existence of weak solutions in a general setting of reaction-cross diffusion systems, as well as some qualitative properties of the solutions. This is a joint work with L. Desvillettes, Th. Lepoutre and A....

Read More

Well-posedness for viscous compressible fluids with only bounded density

Event Date: Mar 11, 2019 in CAPDE, Seminars

Abstract: In this talk, we consider the well-posedness issue for the barotropic Navier-Stokes equations. We consider initial velocity fields which have (slightly) sub-critical regularity, and initial densities which are (essentially) only bounded; in particular, we can consider densities having discontinuities across an interface. We are able to establish a local in time existence and uniqueness result in any space dimension, generalising previous results due to Hoff. The proof combines a maximal regularity approach with the study of propagation of geometric structures, in the same spirit of...

Read More

On Kac’s model, ideal Thermostats, and finite Reservoirs

Event Date: Dec 03, 2018 in CAPDE, Núcleo Modelos Estocásticos de Sistemas Complejos y Desordenados, Seminars

Abstract:   In 1956, Mark Kac introduced a stochastic model to derive a Boltzmann-like equation. Like the space-homogeneous Boltzmann’s  equation, Kac’s equation is ergodic with centered Gaussians as the  unique equilibrium state. In this talk, I will introduce Kac’s model, the thermostat used in [1] to guarantee exponentially fast convergence to equilibrium, and sketch the result in [2] how this infinite  thermostat can be approximated by a finite but large reservoir. References: [1]Bonetto, F., Loss, M.,Vaidyanathan, R.: J. Stat. Phys. 156(4), 647– 667 (2014) [2]Bonetto...

Read More

Well-posedness and long time behavior for the Schrödinger-Korteweg-de Vries interactions on the half-Line

Event Date: Nov 19, 2018 in CAPDE, Seminars

Abstract:   In this talk we discuss about the initial-boundary value problem for the Schrödinger-Korteweg-de Vries system on the left and right half-line for a wide class of initial-boundary data, including the energy regularity H1(R±) × H1(R±) for initial data. Assuming homogeneous boundary conditions it is shown for positive coupling interactions that local solutions can be extended globally in time for initial data in the energy space; furthermore, for negative coupling interactions it was proved, for a certain class of regular initial data, the following result: if the respective...

Read More

Resonances in deformed tubes: twisting and bending & Gross-Pitaevskii equation and integrable systems

Event Date: Nov 12, 2018 in CAPDE, Seminars

16:00 hrs.   Expositor Pablo Miranda, (USach) Título Resonances in deformed tubes: twisting and bending Abstract: In this talk we will consider  an infinite straight tube and  we will deform it  by a periodic twisting and a local bending. On the deformed tube we will define the Laplacian and will study the existence of scattering resonances created by the deformations. We will show the existence of exactly one resonance or one eigenvalue near the bottom of the essential spectrum, depending on the strength of the twisting and the bending. We will also obtain the asymptotic behavior of the...

Read More