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 ...

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 ...

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 ...

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 ...

We analyze a model optimal control problem for a 2D scalar conservation law-the so-called inverse design problem-with the goal being to identify the initial datum leading to a given final time configuration. The presence ...

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 ...

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, ...

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 ...

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, ...

We present a guidance by repulsion model based on a driver-evader interaction where the driver, assumed to be faster than the evader, follows the evader but cannot be arbitrarily close to it, and the evader tries to move ...