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We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…
This paper presents boundary observer design for space and time dependent reaction-advection-diffusion equations using backstepping method. The method uses only a single measurement at the boundary of the systems. The existence of the…
The structure, linear stability, and dynamics of localized solutions to singularly perturbed reaction-diffusion equations has been the focus of numerous rigorous, asymptotic, and numerical studies in the last few decades. However, with a…
The problem of estimating the reaction coefficient of a system governed by a reaction-diffusion partial differential equation is tackled. An estimator relying on boundary measurements only is proposed. The estimator is based upon a setpoint…
This paper studies the design of a finite-dimensional output feedback controller for the stabilization of a reaction-diffusion equation in the presence of a sector nonlinearity in the boundary input. Due to the input nonlinearity, classical…
An understanding of the hydrodynamics of multiphase processes is essential for their design and operation. Multiphase computational fluid dynamics (CFD) simulations enable researchers to gain insight which is inaccessible experimentally.…
Atomistic computer simulations are applied to investigate the atomic structure, thermal stability, and diffusion processes in Al-Si interphase boundaries as a prototype of metal-ceramic interfaces in composite materials. Some of the most…
This paper investigates the output feedback setpoint regulation control of a reaction-diffusion equation by means of boundary control. The considered reaction-diffusion plant may be open-loop unstable. The proposed control strategy consists…
The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial…
In this paper, we consider the large-time behavior of solutions of a reaction diffusion system arising from a nuclear reactor model with the Robin boundary conditions, which consists of two real-valued unknown functions. In particular, we…
This is the first part of our study of inertial manifolds for the system of 1D reaction-diffusion-advection equations which is devoted to the case of Dirichlet or Neumann boundary conditions. Although this problem does not initially possess…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
We study the well-posedness of a nonlinear reaction diffusion partial differential equation system on the half-line coupled with a stochastic dynamical boundary condition, a random system arising from the description of the chemical…
Modeling microstructure evolution in electrochemical systems is vital for understanding the mechanism of various electrochemical processes. In this work, we propose a general phase field framework that is fully variational and thus…
Cataloging the complex behaviors of dynamical systems can be challenging, even when they are well-described by a simple mechanistic model. If such a system is of limited analytical tractability, brute force simulation is often the only…
In this paper, we consider the stochastic optimal control problem for the interacting particle system. We obtain the stochastic maximum principle of the optimal control system by introducing a generalized backward stochastic differential…
Many chemical and biological experiments involve multiple treatment factors and often it is convenient to fit a nonlinear model in these factors. This nonlinear model can be mechanistic, empirical or a hybrid of the two. Motivated by…
The paper discusses the use of amplitude equations to describe the spatio-temporal dynamics of a chemical reaction-diffusion system based on an Oregonator model of the Belousov-Zhabotinsky reaction. Sufficiently close to a supercritical…
Reaction-diffusion systems driven far from thermodynamic equilibrium through the injection of energy can support multiple distinct spatial patterns that persist as long-lived dynamical phases. The stability of these metastable phases is not…
In recent years considerable portion of the computer science community has focused its attention on understanding living cell biochemistry and efforts to understand such complication reaction environment have spread over wide front, ranging…