相关论文: Remarks on the Controllability of Some Quasilinear…

In this paper we establish the theory on semiglobal classical solution to first order quasilinear hyperbolic systems with a kind of nonlocal boundary conditions, and based on this, the corresponding exact boundary controllability and…

This work addresses controllability properties for some systems of partial differential equations in which the main feature is the coupling through nonlocal integral terms. In the first part, we study a nonlinear parabolic-elliptic system…

In this article we study a controllability problem for a parabolic and a hyperbolic partial differential equations in which the control is the shape of the domain where the equation holds. The quantity to be controlled is the trace of the…

The goal of this note is to study nonlinear parabolic problems nonlocal in time and space. We first establish the existence of a solution and its uniqueness in certain cases. Finally we consider its asymptotic behaviour.

In this paper, we propose quasilinearization methods that convert nonlocal fully-nonlinear parabolic systems into the nonlocal quasilinear parabolic systems. The nonlocal parabolic systems serve as important mathematical tools for modelling…

This paper extends our previous controllability results for a class of coupled linear parabolic systems with nonlocal interactions, motivated by applications in finance such as generalized Black--Scholes models. We establish local null…

This paper deals with the analysis of the internal control with constraint of positive kind of a parabolic PDE with nonlinear diffusion when the time horizon is large enough. The minimal controllability time will be strictly positive. We…

This paper deals with the insensitizing controllability property of the quasilinear parabolic equation with dynamic boundary conditions. This problem can be reformulated as a null controllability problem for a cascade quasilinear system…

The null-timelike initial-boundary value problem for a hyperbolic system of equations consists of the evolution of data given on an initial characteristic surface and on a timelike worldtube to produce a solution in the exterior of the…

We study local and global existence of solutions for some semilinear parabolic initial boundary value problems with autonomous nonlinearities having a "Newtonian" nonlocal term.

This paper proposes an optimal control problem for a parabolic equation with a nonlocal nonlinearity. The system is described by a parabolic equation involving a nonlinear term that depends on the solution and its integral over the domain.…

The aim of this paper is to study the null controllability of a class of quasilinear parabolic equations. In a first step we prove that the associated linear parabolic equations with non-constant diffusion coefficients are approximately…

This review surveys previous and recent results on null controllability and inverse problems for parabolic systems with dynamic boundary conditions. We aim to demonstrate how classical methods such as Carleman estimates can be extended to…

We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time…

In this paper, we are concerned with local controllability properties of degenerate parabolic equations in bounded domains that evolve in time. More precisely, we deal with the exact controllability to a positive trajectory of a…

This paper is concerned with the null controllability problem for a class of quasilinear parabolic equations under multiplicative control, locally supported in space. For the purpose of proving the existence of a multiplicative control…

This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…

We consider the temporal periodic solutions to general nonhomogeneous quasilinear hyperbolic equations with a kind of weak diagonal dominant structure. Under the temporal periodic boundary conditions, the existence, stability and uniqueness…

In this paper, we establish the existence of solutions for a particular class of degenerate hyperbolic equations. Following this, we approximate these degenerate equations by employing a sequence of uniformly hyperbolic equations. Notably,…

This paper addresses the controllability of a class of quasi-linear parabolic equations governed by multiplicative controls with mobile support. To prove the existence of such a control forcing the solution to rest at time $T>0$, we first…