We derive a formula for the n-row Macdonald polynomials with the coefficients presented both combinatorically and in terms of very-well-poised hypergeometric series.

We introduce and analyze a stable procedure for the approximation of 〈f†, φ〉 where f† is the least residual norm solution of the minimal norm of the ill-posed equation Af = g, with compact operator A : X → Y between Hilbert spaces, and φ ∈ X has some smoothness assumption. Our method is based on a finite number of singular values of A and some finite rank operators. Our results are in a more ge...

This paper is concerned with the mathematical analysis of the time-domain Maxwell equations in a three-dimensional open cavity. An exact transparent boundary condition is developed to reformulate the open cavity scattering problem in an unbounded domain, equivalently, into an initial-boundary value problem in a bounded domain. The well-posedness and stability are studied for the reduced problem...

We prove the well-posedness of entropy weak solutions of a scalar conservation law with non-local flux arising in traffic flow modeling. The result is obtained providing accurate L∞, BV and L estimates for the sequence of approximate solutions constructed by an adapted Lax-Friedrichs scheme.

We prove global well-posedness for the defocusing cubic wave equation

This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The fluids are acted on by gravity in the ...

This paper deals with the problem of existence of Berge and Berge–Nash equilibria. Abalo and Kostreva have proved existence theorems of Berge and Berge–Nash equilibria for S-equi-well-posed and (S, σ)equi-well-posed games, namely, Theorems 3.2–3.3 [Abalo, K.Y., Kostreva, M.M., 1996. Fixed Points, Nash Games and their Organization. Topological Methods in Nonlinear Analysis 8, 205–215.]. In this ...

We consider the conformal Einstein equations for massless colli-sionless gas cosmologies which admit an isotropic singularity. After developing the general theory, we restrict to spatially-homogeneous cosmologies. We show that the Cauchy problem for these equations is well-posed with data consisting of the limiting particle distribution function at the singularity.

We discuss a Hilbert space method that allows to prove analytical well-posedness of a class of linear strongly damped wave equations. The main technical tool is a perturbation lemma for sesquilinear forms, which seems to be new. In most common linear cases we can furthermore apply a recent result due to Crouzeix–Haase, thus extending several known results and obtaining optimal analyticity angle.

Initial-boundary value problems for 1-dimensional ‘completely integrable’ equations can be solved via an extension of the inverse scattering method, which is due to Fokas and his collaborators. A crucial feature of this method is that it requires the values of more boundary data than given for a well-posed problem. In the case of cubic NLS, knowledge of the Dirichet data suffices to make the pr...