Former Research Lines
http://hdl.handle.net/20.500.11824/21
Sat, 28 May 2022 17:08:33 GMT2022-05-28T17:08:33ZA 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.
Sat, 01 Jul 2017 00:00:00 GMThttp://hdl.handle.net/20.500.11824/7132017-07-01T00:00:00ZA 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.
Thu, 01 Jun 2017 00:00:00 GMThttp://hdl.handle.net/20.500.11824/6802017-06-01T00:00:00ZSpherically symmetric solutions to a model for phase transitions driven by configurational forces
http://hdl.handle.net/20.500.11824/593
Spherically symmetric solutions to a model for phase transitions driven by configurational forces
Ou, Y.; Zhu, P.
We prove the global-in-time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear, non-uniformly parabolic equation of second order. This problem models the evolutional behavior of materials in which martensitic phase transitions, driven by configurational forces, take place. Moreover, it can be considered to be a regularization of the corresponding sharp interface model. By assuming that the solutions are spherically symmetric, we reduce the original multi-dimensional problem to the one in one space dimension, then prove the existence of spherically symmetric solutions. Our proof is valid due to the essential feature that the resulting problem is one-dimensional.
Sat, 31 Dec 2011 00:00:00 GMThttp://hdl.handle.net/20.500.11824/5932011-12-31T00:00:00ZApproximation of Hölder continuous homeomorphisms by piecewise affine homeomorphisms
http://hdl.handle.net/20.500.11824/602
Approximation of Hölder continuous homeomorphisms by piecewise affine homeomorphisms
Bellido, J.C.; Mora-Corral, C.
This paper is concerned with the problem of approximating a homeomorphism by piecewise affine homeomorphisms. The main result is as follows: every homeomorphism from a planar domain with a polygonal boundary to ℝ2 that is globally Hölder continuous of exponent α ∈ (0, 1], and whose inverse is also globally Hölder continuous of exponent α can be approximated in the Hölder norm of exponent β by piecewise affine homeomorphisms, for some β ∈ (0,α) that only depends on α. The proof is constructive. We adapt the proof of simplicial approximation in the supremum norm, and measure the side lengths and angles of the triangulation over which the approximating homeomorphism is piecewise affine. The approximation in the supremum norm, and a control on the minimum angle and on the ratio between the maximum and minimum side lengths of the triangulation suffice to obtain approximation in the Hölder norm.
Sat, 31 Dec 2011 00:00:00 GMThttp://hdl.handle.net/20.500.11824/6022011-12-31T00:00:00Z