Related papers: Nonlinear semigroups with unbounded generators und…

We study the extension of integrable equations which possess the Lax representations to noncommutative spaces. We construct various noncommutative Lax equations by the Lax-pair generating technique and the Sato theory. The Sato theory has…

We develop a nonlinear evolution framework for nonlinear parabolic equations with unbounded drift terms formulated in Lorentz spaces. The main contribution lies in the construction of uniformly m-accretive operators based on Lorentz-Sobolev…

The linearity inherent in quantum mechanics limits current quantum hardware from directly solving nonlinear systems governed by nonlinear differential equations. One can opt for linearization frameworks such as Carleman linearization, which…

When we are interested in the long-term behaviour of solutions to linear evolution equations, a large variety of techniques from the theory of $C_0$-semigroups is at our disposal. However, if we consider for instance parabolic equations…

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. A…

In this paper, we present a new Carleman estimate for the adjoint equations associated to a class of super strong degenerate parabolic linear problems. Our approach considers a standard geometric imposition on the control domain, which can…

This contribution to the Proceedings of the Workshop on Integrable Theories, Solitons and Duality in Sao Paulo in July 2002 summarizes results from the papers hep-th/0112023 and math.QA/0208043. We derive the non-local conserved charges in…

We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…

The paper is devoted to evolution equations of the form $\partial$ $\partial$t u(t) = --(A + B(t))u(t), t $\in$ I = [0, T ], on separable Hilbert spaces where A is a non-negative self-adjoint operator and B($\times$) is family of…

This paper presents Carleman-Fourier linearization for analyzing nonlinear real dynamical systems with periodic vector fields. Using Fourier basis functions, this novel framework transforms such dynamical systems into equivalent…

Semigroups, generated by Feller processes killed upon leaving a given domain, are considered. These semigroups correspond to Cauchy-Dirichlet type initial-exterior value problems in this domain for a class of evolution equations with…

Matrix concentration inequalities provide information about the probability that a random matrix is close to its expectation with respect to the $l_2$ operator norm. This paper uses semigroup methods to derive sharp nonlinear matrix…

This survey describes the method of approximation of operator semigroups, based on the Chernoff theorem. We outline recent results in this domain as well as clarify relations between constructed approximations, stochastic processes,…

We give a characterization for two different concepts of quasi-analyticity in Carleman ultraholomorphic classes of functions of several variables in polysectors. Also, working with strongly regular sequences, we establish generalizations of…

Carleman linearization is a mathematical technique that transforms nonlinear dynamical systems into infinite-dimensional linear systems, enabling simplified analysis. Initially developed for ordinary differential equations (ODEs) and later…

We revisit the method of Carleman linearization for systems of ordinary differential equations with polynomial right-hand sides. This transformation provides an approximate linearization in a higher-dimensional space through the exact…

We propose a globally convergent numerical method to compute solutions to a general class of quasi-linear PDEs with both Neumann and Dirichlet boundary conditions. Combining the quasi-reversibility method and a suitable Carleman weight…

This work focuses on non-compact groups and their applications to quantum gravity, mainly through the use of tensor operators. First, the mathematical theory of tensor operators for a Lie group is recast in a new way which is used to…

In this note the Chernoff Theorem is used to approximate evolution semigroups constructed by the procedure of subordination. The considered semigroups are subordinate to some original, unknown explicitly but already approximated by the same…

We present new convergence analyses for parallel subspace correction methods for unconstrained semicoercive and nearly semicoercive convex optimization problems, generalizing the theory of singular and nearly singular linear problems to a…