相关论文: Controllability of some semilinear shadow reaction…
The close-to-equilibrium regularity of solutions to a class of reaction-diffusion systems is investigated. The considered systems typically arise from chemical reaction networks and satisfy a complex balanced condition. Under some…
We present a control design for semilinear and quasilinear 2x2 hyperbolic partial differential equations with the control input at one boundary and a nonlinear ordinary differential equation coupled to the other. The controller can be…
We consider the control problem of the heat equation on bounded and unbounded domains, and more generally the corresponding inhomogeneous equation for the Schr\"odinger semigroup. We show that if the sequence of null-controls associated to…
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 show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient…
We prove a priori bounds for solutions of stochastic reaction diffusion equations with super-linear damping in the reaction term. These bounds provide a control on the supremum of solutions on any compact space-time set which only depends…
Families of regimes for discrete control systems are studied possessing a special quasi-controllability property that is similar to the Kalman controllability property. A new approach is proposed to estimate the amplitudes of transient…
We demonstrate that the cross sections derived from the "shadow model" for reactions between light nuclei disagree with low-energy laboratory data and exhibit unphysical behavior at energies below those for which data exist. As a…
In this work, we study the global existence of solutions for a class of semilinear nonlocal reaction-diffusion systems with $m$ components on a bounded domain $\Omega$ in $\mathbb{R}^n$ with smooth boundary. The initial data is assumed to…
We consider a system of particles undergoing correlated diffusion with elastic boundary conditions on the half-line. By taking the large particle limit we establish existence and uniqueness for the limiting empirical measure valued process…
Controlling illumination in images is essential for photography and visual content creation. While closed-source models have demonstrated impressive illumination control, open-source alternatives either require heavy control inputs like…
We study the blow up solutions of a semilinear reaction diffusion system coupled in both equations and boundary conditions. The main purpose is to understand how the reaction terms and the absorption terms affect the blow-up properties. We…
This paper discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design…
Boundary characteristic point regularity is studied for a class of semilinear heat equations and an ODE criterion of regularity is obtained. Extensions to higher-order semilinear parabolic problems are discussed.
The rigorous asymptotics from reaction-cross-diffusion systems for three species with known entropy to cross-diffusion systems for two variables is investigated. The equations are studied in a bounded domain with no-flux boundary…
We present a new result about the shadowing of nontransversal chain of heteroclinic connections based on the idea of dropping dimensions. We illustrate this new mechanism with several examples. As an application we discuss this mechanism in…
The fast reaction limit for a nonlinear bulk-surface reaction-diffusion system is investigated. This system describes a reversible reaction with arbitrary stoichiometric coefficients, where one chemical is present in a bounded vessel…
A small-gain approach is proposed to analyze closed-loop stability of linear diffusion-reaction systems under finite-dimensional observer-based state feedback control. For this, the decomposition of the infinite-dimensional system into a…
We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction. We understand the linear reaction-diffusion system as a gradient flow of the free energy in the…
We study the controllability of a coupled system of linear parabolic equations, with non-negativity constraint on the state. We establish two results of controllability to trajectories in large time: one for diagonal diffusion matrices with…