Former Research Lines
http://hdl.handle.net/20.500.11824/21
2023-12-09T17:45:32ZA splitting method for the augmented Burgers equation
http://hdl.handle.net/20.500.11824/713
A splitting method for the augmented Burgers equation
Ignat, L.I.; Pozo, A.
In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of ﬁrst order. We also analyze the large-time behavior of the approximated solution by obtaining the ﬁrst term in the asymptotic expansion. We prove that, when time increases, these solutions be have as the self-similar solutions of the viscous Burgers equation.
2017-07-01T00:00:00ZA semi-discrete large-time behavior preserving scheme for the augmented Burgers equation
http://hdl.handle.net/20.500.11824/680
A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation
Ignat, L.I.; Pozo, A.
In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain $L^1-L^p$ decay rates. The asymptotic behavior of the solution is obtained by showing that the influence of the convolution term $K*u_{xx}$ is the same as $u_{xx}$ for large times. Then, we propose a semi-discrete numerical scheme that preserves this asymptotic behavior, by introducing two correcting factors in the discretization of the non-local term. Numerical experiments illustrating the accuracy of the results of the paper are also presented.
2017-06-01T00:00:00ZNematic elastomers: Gamma-limits for large bodies and small particles
http://hdl.handle.net/20.500.11824/597
Nematic elastomers: Gamma-limits for large bodies and small particles
Cesana, P.
We compute the large-body and the small-particle Gamma-limit of a family of energies for nematic elastomers. We work under the assumption of small deformations (linearized kinematics) and consider both compressible and incompressible materials. In the large-body asymptotics, even if we describe the local orientation of the liquid crystal molecules according to the model of perfect order (Frank theory), we prove that we obtain a fully biaxial nematic texture (that of the de Gennes theory) as a by-product of the relaxation phenomenon connected to Gamma-convergence. In the case of small particles, we show that formation of new microstructure is not possible, and we describe the map of minimizers of the Gamma-limit as the phase diagram of the mechanical model.
2011-12-31T00:00:00ZWell-posedness in critical spaces for the system of compressible Navier-Stokes in larger spaces
http://hdl.handle.net/20.500.11824/589
Well-posedness in critical spaces for the system of compressible Navier-Stokes in larger spaces
Haspot, B.
This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N≥2. We address the question of well-posedness for large data having critical Besov regularity. Our result improves the analysis of R. Danchin (2007) in [13], of Q. Chen et al. (2010) in [8] and of B. Haspot (2009, 2010) in [15,16] inasmuch as we may take initial density in Bp,1Np with 1≤p<+∞. Our result relies on a new a priori estimate for the velocity, where we introduce a new unknown called effective velocity to weaken one the coupling between the density and the velocity. In particular for the first time we obtain uniqueness without imposing hypothesis on the gradient of the density.
2011-12-31T00:00:00Z