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A splitting method for the augmented Burgers equation
(2017-07-01)
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 ...
A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation
(2017-06-01)
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 ...
On the response of autonomous sweeping processes to periodic perturbations
(2016-12-01)
If $x_0$ is an equilibrium of an autonomous differential equation $\dot x=f(x)$ and $\det \|f'(x_0)\|\not=0$, then $x_0$ persists under autonomous perturbations and $x_0$ transforms into a $T$-periodic solution under ...
A direct algorithm in some free boundary problems
(2016-06-28)
In this paper we propose a new algorithm for the well known elliptic obstacle problem and for parabolic variational inequalities like one and two phase Stefan problem and of obstacle type. Our approach enters the category ...
Dispersion for 1-d Schrödinger and wave equations with bv coefficients
(2016-01-01)
In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the ...
Hardy type inequalities for $\Delta_{\lambda}$-Laplacians
(2016-01-01)
We derive Hardy-type inequalities for a large class of sub-elliptic operators that belong to the class of $\Delta_{\lambda}$-Laplacians and find explicit values for the constants involved. Our results generalize previous ...
Time asymptotics for a critical case in fragmentation and growth-fragmentation equations
(2016-01-01)
Fragmentation and growth-fragmentation equations is a family of problems with varied and wide applications. This paper is devoted to the description of the long-time asymptotics of two critical cases of these equations, ...
Numerical meshes ensuring uniform observability of one-dimensional waves: Construction and analysis
(2016-01-01)
We build nonuniform numerical meshes for the finite difference and finite element approximations of the one-dimensional wave equation, ensuring that all numerical solutions reach the boundary, as continuous solutions do, ...
An ADER-type scheme for a class of equations arising from the water-wave theory
(2016-01-01)
In this work we propose a numerical strategy to solve a family of partial differential equations arising from the water-wave theory. These problems may contain four terms; a source which is an algebraic function of the ...
Output feedback of Markov jump linear systems with no mode observation: An automotive throttle application
(2016-01-01)
Summary The note presents an output feedback control strategy for Markov jump linear systems with no mode observation. Based on minimizing a finite-time quadratic cost, we derive an algorithm that generates output feedback ...