Related papers: Continuous dependence on data for linear evolution…

This work deals with the exponential stabilization of a system of three semilinear parabolic partial differential equations (PDEs), written in a strict feedforward form. The diffusion coefficients are considered distinct and the PDEs are…

We revisit the classical issue of the controllability/observability cost of linear first order evolution systems, starting with ODEs, before turning to some linear first order evolution PDEs in several space dimensions, including hyperbolic…

We propose a computer-assisted approach to studying the effective continuum behavior of spatially discrete evolution equations. The advantage of the approach is that the "coarse model" (the continuum, effective equation) need not be…

We establish existence and uniqueness of global, bounded weak solutions to quasilinear PDEs with bounded, uniformly continuous initial data and investigate their properties. Moreover, we establish existence of bounded weak solutions when…

We propose a gate-based quantum algorithm for the prediction step of Bayesian state estimation based on the Fokker-Planck equation on a discretized position-velocity state space. The probability density is encoded in the amplitudes of a…

We establish local well-posedness for the higher-order nonlinear Schr\"odinger equation, formulated on the half-line. We consider the scenario of associated coefficients such that only one boundary condition is required, which is assumed to…

In the present paper we discuss problems concerning evolutions of densities related to Ito diffusions in the framework of the statistical exponential manifold. We develop a rigorous approach to the problem, and we particularize it to the…

Integrating evolutionary partial differential equations (PDEs) is an essential ingredient for studying the dynamics of the solutions. Indeed, simulations are at the core of scientific computing, but their mathematical reliability is often…

In our previous studies, we developed discrete-space Birth, Death and Innovation Models (BDIM) of genome evolution. These models explain the origin of the characteristic Pareto distribution of paralogous gene family sizes in genomes, and…

In this note, we review some of the recent developments in the well-posedness theory of nonlinear dispersive partial differential equations with random initial data.

High-dimensional partial-differential equations (PDEs) arise in a number of fields of science and engineering, where they are used to describe the evolution of joint probability functions. Their examples include the Boltzmann and…

A multi-phase-field model for the description of the discontinuous precipitation reaction is formulated which takes into account surface diffusion along grain boundaries and interfaces as well as volume diffusion. Simulations reveal that…

The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

A large class of initial-boundary value problems of linear evolution partial differential equations formulated on the half-line is analyzed via the unified transform method. In particular, explicit formulae are presented for the generalized…

We demonstrate the use of the Unified Transform Method or Method of Fokas for boundary value problems for systems of constant-coefficient linear partial differential equations. We discuss how the apparent branch singularities typically…

We present a method to solve initial-boundary value problems for linear and integrable nonlinear differential-difference evolution equations. The method is the discrete version of the one developed by A. S. Fokas to solve initial-boundary…

We study the Muskat problem on the half-plane, which models motion of an interface between two fluids of distinct densities (e.g., oil and water) in a porous medium (e.g., an aquifer) that sits atop an impermeable layer (e.g., bedrock).…

Usually, the systems of partial differential equations (PDEs) are discovered from observational data in the single vector equation form. However, this approach restricts the application to the real cases, where, for example, the form of the…

Deriving evolution equations accounting for both anomalous diffusion and reactions is notoriously difficult, even in the simplest cases. In contrast to normal diffusion, reaction kinetics cannot be incorporated into evolution equations…