In this review, concerning parabolic equations, we give self-contained descriptions on (1)
derivations of Carleman estimates;(2) methods for applications of the Carleman estimates to …

Even if numerical simulation of the Burgers' equation is well documented in the literature, a
detailed literature survey indicates that gaps still exist for comparative discussion regarding …

Among various interesting topics in partial differential equations, the theory of parabolic
equations could be singled out for at least one feature: it provides ground for the interaction …

We deal with the problem of approximating a scalar conservation law by a conservation law
with nonlocal flux. As convolution kernel in the nonlocal flux, we consider an exponential …

In this paper, we deal with controllability properties of linear and nonlinear Korteweg–de
Vries equations in a bounded interval. The main part of this paper is a result of uniform …

The adjoint method provides a computationally efficient means of calculating the gradient for
applications in constrained optimization. In this article, we consider a network of scalar …

We revisit a result by Coron and Guerrero stating that the one-dimensional transport-
diffusion equation controlled by the left Dirichlet boundary value is zero-controllable at a …

Conservation and balance laws on networks have been the subject of much research
interest given their wide range of applications to real-world processes, particularly traffic …

We construct explicit time-varying feedback laws leading to the global (null) stabilization in
small time of the viscous Burgers equation with three scalar controls. Our feedback laws use …

In this paper, we deal with both nonviscous and viscous Burgers-type equations on a
bounded interval. We study the global exact controllability of these equations when we have …