Former Research Lineshttp://hdl.handle.net/20.500.11824/212021-09-22T14:43:36Z2021-09-22T14:43:36ZA splitting method for the augmented Burgers equationIgnat, L.I.Pozo, A.http://hdl.handle.net/20.500.11824/7132021-07-08T07:03:47Z2017-07-01T00:00:00ZA 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 equationIgnat, L.I.Pozo, A.http://hdl.handle.net/20.500.11824/6802021-07-08T07:03:47Z2017-06-01T00:00:00ZA 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.
2017-06-01T00:00:00ZDispersive Properties for Discrete Schrödinger EquationsIgnat, L.I.Stan, D.http://hdl.handle.net/20.500.11824/6082021-07-08T07:03:39Z2011-12-31T00:00:00ZDispersive Properties for Discrete Schrödinger Equations
Ignat, L.I.; Stan, D.
In this paper we prove dispersive estimates for the system formed by two coupled discrete Schrödinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting absorption principle. The decay of the solutions is proved by using classical and some new results on oscillatory integrals.
2011-12-31T00:00:00ZSolvability via viscosity solutions for a model of phase transitions driven by configurational forcesZhu, P.http://hdl.handle.net/20.500.11824/5882021-07-08T07:03:38Z2011-12-31T00:00:00ZSolvability via viscosity solutions for a model of phase transitions driven by configurational forces
Zhu, P.
This article is concerned with an initial-boundary value problem for an elliptic-parabolic coupled system arising in martensitic phase transition theory of elastically deformable solid materials, e.g., steel. This model was proposed in Alber and Zhu (2007) [4], and investigated in Alber and Zhu (2006) [3] the existence of weak solutions which are defined in a standard way, however the key technique used in Alber and Zhu (2006) [3] is not applicable to multi-dimensional problem. One of the motivations of this study is to solve this multi-dimensional problem, and another is to investigate the sharp interface limits. Thus we define weak solutions in a way, which is different from Alber and Zhu (2006) [3], by using the notion of viscosity solution. We do prove successfully the existence of weak solutions in this sense for one-dimensional problem, yet the multi-dimensional problem is still open.
2011-12-31T00:00:00Z