Related papers: Computing Solution Operators of Boundary-value Pro…
A computational method for numeric resolution of a PDEs system, based on a Finite Differences schema integrated by interpolations of partial results, and an estimate of the error of its solution respect to the normal FD solution.
A multi-cube method is developed for solving systems of elliptic and hyperbolic partial differential equations numerically on manifolds with arbitrary spatial topologies. It is shown that any three-dimensional manifold can be represented as…
In the theory and practice of inverse problems for partial differential equations (PDEs) much attention is paid to the problem of the identification of coefficients from some additional information. This work deals with the problem of…
We present an algorithm for the numerical solution of systems of fully nonlinear PDEs using stochastic coded branching trees. This approach covers functional nonlinearities involving gradient terms of arbitrary orders, and it requires only…
A solution to the suboptimal $H^\infty$-control problem is given for a class of hyperbolic partial differential equations (PDEs). The first result of this manuscript shows that the considered class of PDEs admits an equivalent…
The numerical solution of differential equations can be formulated as an inference problem to which formal statistical approaches can be applied. However, nonlinear partial differential equations (PDEs) pose substantial challenges from an…
Partial Differential Equations (PDEs) are fundamental tools for modeling physical phenomena, yet most PDEs of practical interest cannot be solved analytically and require numerical approximations. The feasibility of such numerical methods,…
We consider the Dirac operator on globally hyperbolic manifolds with timelike boundary and show well-posedness of the Cauchy initial-boundary value problem coupled to MIT-boundary conditions. This is achieved by transforming the problem…
We study the Cauchy problem for fully nonlinear (stochastic) parabolic partial differential equations. We provide both in deterministic and stochastic case the existence of a maximal defined solution for the problem and we provide suitable…
Quantum algorithms to integrate nonlinear PDEs governing flow problems are challenging to discover but critical to enhancing the practical usefulness of quantum computing. We present here a near-optimal, robust, and end-to-end quantum…
This paper deals with the boundary value problems for the singularly perturbed differential-algebraic system of equations. The case of turning points has been studied. The sufficient conditions for existence and uniqueness of the solution…
We propose a finite-dimensional control-based method to approximate solution operators for evolutional partial differential equations (PDEs), particularly in high-dimensions. By employing a general reduced-order model, such as a deep neural…
This paper studies the Cauchy problem for variable coefficient weakly hyperbolic first order systems of partial differential operators. The hyperbolicity assumption is that for each $t, x$ the principal symbol is hyperbolic. No hypothesis…
Integration of nonlinear partial differential equations with the help of the non-commutative integration over octonions is studied. An apparatus permitting to take into account symmetry properties of PDOs is developed. For this purpose…
We derive new boundary conditions and implementation procedures for nonlinear initial boundary value problems that lead to energy and entropy bounded solutions. A step-by-step procedure for general nonlinear hyperbolic problems on…
First-order systems of hyperbolic partial differential equations (PDEs) occur ubiquitously throughout computational physics, commonly used in simulations of fluid turbulence, shock waves, electromagnetic interactions, and even general…
We study a class of hyperbolic Cauchy problems, associated with linear operators and systems with polynomially bounded coefficients, variable multiplicities and involutive characteristics, globally defined on R^n. We prove well-posedness in…
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…
We introduce a general algebraic setting for describing linear boundary problems in a symbolic computation context, with emphasis on the case of partial differential equations. The general setting is then applied to the Cauchy problem for…
The boundary-value problem on semi-axis for one class operator-differential equations of the fourth order, the main part of which has the multiple characteristic is investigated in this paper in Sobolev type weighted space. Correctness and…