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We summarize researches - in great deal jointly with my host Y. Sarantopoulos and his PhD. students V. Anagnostopoulos and A. Pappas - started by a Marie Curie fellowship in 2001 and is still continuing. The project was to study…
We wish to draw attention to an interesting and promising interaction of two theories. On the one hand, it is the theory of \textbf{pseudo-triangulations} which was useful for implicit solution of thecarpenter's rule problem and proved…
In this work, we provide a deep investigation of a family of arbitrary high order numerical methods for hyperbolic partial differential equations (PDEs), with particular emphasis on very high order versions, i.e., with order higher than 5.…
A hyperbolic system approach is proposed for robust computation of anisotropic diffusion equations that appear in quasineutral plasmas. Though the approach exhibits merits of high extensibility and accurate flux computation, the…
In this paper we outline a general method for finding well-posed boundary value problems for linear equations of mixed elliptic and hyperbolic type, which extends previous techniques of Berezanskii, Didenko, and Friedrichs. This method is…
This paper is devoted to the study of time-dependent hyperbolic systems and the derivation of dispersive estimates for their solutions. It is based on a diagonalisation of the full symbol within adapted symbol classes in order to extract…
This paper develops a probabilistic numerical method for solution of partial differential equations (PDEs) and studies application of that method to PDE-constrained inverse problems. This approach enables the solution of challenging inverse…
A new approach is introduced for deriving a mixed variational formulation for Kirchhoff plate bending problems with mixed boundary conditions involving clamped, simply supported, and free boundary parts. Based on a regular decomposition of…
The 'tHooft-Polyakov monopole is treated as constrained system using the Hamilton-Jacobi method. The set of the Hamilton-Jacobi partial differential equations and the equations of motion are obtained. The quantization of the system is also…
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…
In this study linear and nonlinear higher order singularly perturbed problems are examined by a numerical approach, the differential quadrature method. Here, the main idea is using Chebyshev polynomials to acquire the weighting coefficient…
A number of physical phenomena are described by nonlinear hyperbolic equations. Presence of discontinuous solutions motivates the necessity of development of reliable numerical methods based on the fundamental mathematical properties of…
Building upon previous works by Young, Chernov-Zhang and Bruin-Melbourne-Terhesiu, we present a general scheme to improve bounds on the statistical properties (in particular, decay of correlations, and rates in the almost sure invariant…
This book is an introduction to hyperbolic geometry in dimension three, and its applications to knot theory and to geometric problems arising in knot theory. It has three parts. The first part covers basic tools in hyperbolic geometry and…
The purpose of this review paper is the collection, systematization and discussion of recent results concerning the quantization approach to the Jacobian conjecture, as well as certain related topics.
This article addresses linear hyperbolic partial differential equations and pseudodifferential equations with strongly singular coefficients and data, modelled as members of algebras of generalised functions. We employ the recently…
We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian…
This is essentially a survey paper in which we solve the global Cauchy problem on causal manifolds for hyperbolic systems of linear partial differential equations in the framework of hyperfunctions. Besides the classical Cauchy-Kowalevsky…
In this paper, we prove restriction estimates for hyperbolic paraboloids in dimensions $n>=5$ by the polynomial partitioning method.
We consider the problem of decomposing a multivariate polynomial as the difference of two convex polynomials. We introduce algebraic techniques which reduce this task to linear, second order cone, and semidefinite programming. This allows…