Related papers: Remarks on the Whitham equations
This article provides a brief discussion of the functional of super Riemann surfaces from the point of view of classical (i.e. not "super-) differential geometry. The discussion is based on symmetry considerations and aims to clarify the…
Inequalities play an important role in pure and applied mathematics. In particular, Opial inequality plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. It has…
This paper deals with some simple results about spherical functions of type $\delta$, namely new integral formulas, new results about behavior at infinity and some facts about the related $C_\sigma$ functions.
Two methods are explained to exactly solve Maxwell's equations where permittivity, permeability and conductivity may vary in space. In the constitutive relations, retardation is regarded. If the material properties depend but on one…
The wavefunction of a particle is obtained from its intermediate states and interaction processes considered as happening concurrently. When the interaction is described by a potential, the energy of the particle is equal to its total…
We study the homogeneous wave equation with radially symmetric data in four or higher space dimensions. Using some new integral representations for the Riemann operator, we establish weighted decay estimates for the solution.
The Riemann Theorem states, that for any nontrivial connected and simply connected domain on the Riemann sphere there exists some its conformal bijection to the exterior of the unit disk. In this paper we find an explicit form of this map…
Some aspects of adelic generalized functions, as linear continuous functionals on the space of Schwartz-Bruhat functions, are considered. The importance of adelic generalized functions in adelic quantum mechanics is demonstrated. In…
We consider the connection of functional decompositions of rational functions over the real and complex numbers, and a question about curves on a Riemann sphere which are invariant under a rational function.
The modulation equations for Stokes waves in shallow water coupled to wave generated mean flow, derived in Whitham (1967), based on an averaged Lagrangian are revisited. Firstly, it is shown that they can be recast into two coupled…
The semi-classical Korteweg-deVries equation for step-like data is considered with a small parameter in front of the highest derivative. Using perturbation analysis Whitham theory is constructed to higher order. This allows the order one…
We study the wave equation for the gravitational waves in the Randal-Sundrum brane cosmology model. We solve the global Cauchy problem and we establish that the solutions are the sum of a slowly decaying massless wave localized near the…
We present several recent results concerning Cauchy and event horizons. In the first part of the paper we review the differentiablity properties of the Cauchy and the event horizons. In the second part we discuss compact Cauchy horizons and…
This article develops the numerical and theoretical study of a reconstruction algorithm of a potential in a wave equation from boundary measurements, using a cost functional built on weighted energy terms coming from a Carleman estimate.…
In this review paper we stress the importance of the higher transcendental Wright functions of the second kind in the framework of Mathematical Physics.We first start with the analytical properties of the classical Wright functions of which…
In this paper, regularity properties, Strichartz type estimates to solutions of multipo{\i}nt Cauchy problem for linear and nonlinear abstract wave equations in vector-valued function spaces are obtained. The equation includes a linear…
We prove certain mixed-norm Strichartz estimates on manifolds with boundary. Using them we are able to prove new results for the critical and subcritical wave equation in 4-dimensions with Dirichlet or Neumann boundary conditions. We obtain…
We discuss the behavior of harmonic functions on Riemannian cones as defined below and Lioville's theorem.
The main purpose of this note is to provide a topological approach to defining additive functions on Riemannian co-compact normal coverings.
The work studies some Difference equations, which are connected with Mejer's function.