Related papers: Initial-boundary value problems for second order s…
This paper focuses on the two-dimensional Benjamin-Bona-Mahony and Benjamin-Bona-Mahony-Burgers equations with a general flux function. The aim is at the global (in time) well-posedness of the initial-and boundary-value problem for these…
This article addresses the question of involutiveness and discusses the initial value problem for a class of overdetermined systems of partial differential equations which arise in the theory of integrable systems and are defined by…
We consider a class of first-order partial differential operators, acting on the space of ultradifferentiable periodic functions, and we describe their range by using the following conditions on the coefficients of the operators: the…
Here we present an algorithm to find elementary first integrals of rational second order ordinary differential equations (SOODEs). In \cite{PS2}, we have presented the first algorithmic way to deal with SOODEs, introducing the basis for the…
In this paper, we propose second-order sufficient optimality conditions for a very general nonconvex constrained optimization problem, which covers many prominent mathematical programs.Unlike the existing results in the literature, our…
We study hyperbolic systems of one-dimensional partial differential equations under general, possibly non-local boundary conditions. A large class of evolution equations, either on individual 1-dimensional intervals or on general networks,…
The reduction of computational costs in the numerical solution of nonstationary problems is achieved through splitting schemes. In this case, solving a set of less computationally complex problems provides the transition to a new level in…
We study an abstract class of autonomous differential inclusions in Hilbert spaces and show the well-posedness and causality, by establishing the operators involved as maximal monotone operators in time and space. Then the proof of the…
We connect boundary conditions for one-sided pseudo-differential operators with the generators of modified one-sided L\'evy processes. On one hand this allows modellers to use appropriate boundary conditions with confidence when restricting…
Complex-linearization of a class of systems of second order ordinary differential equations (ODEs) has already been studied with complex symmetry analysis. Linearization of this class has been achieved earlier by complex method, however,…
This paper establishes an existence theory for discrete second-order boundary value problems on non-uniform time grids using the upper and lower solution method. We consider difference equations of the form $u^{\Delta\Delta}(t_{i-1}) +…
While there exist now formulations of initial boundary value problems for Einstein's field equations which are well posed and preserve constraints and gauge conditions, the question of geometric uniqueness remains unresolved. For two…
In this paper we analyse the well-posedness of the Cauchy problem for a rather general class of hyperbolic systems with space-time dependent coefficients and with multiple characteristics of variable multiplicity. First, we establish a…
We present a framework which enables the analysis of dynamic inverse problems for wave phenomena that are modeled through second-order hyperbolic PDEs. This includes well-posedness and regularity results for the forward operator in an…
We describe a way of solving a partial differential equation using the differential invariants of its point symmetries. By first solving its quotient PDE, which is given by the differential syzygies in the algebra of differential…
We investigate the dependence on parameters for second order difference equations with two point boundary value conditions by using a variational method in case when the corresponding Euler action functional is coercive. Some applications…
This paper is devoted to the analysis of linear second order discrete-time descriptor systems (or singular difference equations (SiDEs) with control). Following the algebraic approach proposed by Kunkel and Mehrmann for pencils of matrix…
We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems respectively…
Variational analysis provides the theoretical foundations and practical tools for constructing optimization algorithms without being restricted to smooth or convex problems. We survey the central concepts in the context of a concrete but…
We consider a rational system of first order difference equations in the plane with four parameters such that all fractions have a common denominator. We study, for the different values of the parameters, the global and local properties of…