Related papers: Remarks on the Whitham equations
We survey some results on Lipschitz and Schauder regularity estimates for viscous Hamilton--Jacobi equations with subcritical L\'evy diffusions. The Schauder estimates, along with existence of smooth solutions, are obtained with the help of…
We present a systematic derivation of the wave kinetic equation describing the dynamics of a statistically inhomogeneous incoherent wave field in a medium with a weak quadratic nonlinearity. The medium can be nonstationary and…
These lecture notes present a computation driven pathway from classical complex analysis to the theory of compact Riemann surfaces and their connections to algebraic geometry. The exposition follows a compute first then abstract philosophy,…
This paper studies variance functions of Cauchy-Stieltjes Kernel families generated by compactly supported centered probability measures. We describe several operations that allow us to construct additional variance functions from known…
Let $\mathcal{H}(b)$ denote the de Branges--Rovnyak space associated with a function $b$ in the unit ball of $H^\infty(\mathbb{C}_+)$. We study the boundary behavior of the derivatives of functions in $\mathcal{H}(b)$ and obtain weighted…
In this study, we obtain some new integral inequalities for different classes of convex functions by using some elementary inequalities and classical inequalities like general Cauchy inequality and Minkowski inequality.
We study modulational stability and instability in the Whitham equation, combining the dispersion relation of water waves and a nonlinearity of the shallow water equations, and modified to permit the effects of surface tension and constant…
In this paper we show how to construct a regular, non commutative Cauchy kernel for slice regular quaternionic functions. We prove an (algebraic) representation formula for such functions, which leads to a new Cauchy formula. We find the…
We consider functional equations (Cauchy's, Abel's and some other functional equations) and show that to find general solution of these equations is equivalent to establish that a space-transformation of a Brownian Motion by suitable…
We study the equational theory of the Weihrauch lattice with composition and iterations, meaning the collection of equations between terms built from variables, the lattice operations $\sqcup$, $\sqcap$, the composition operator $\star$ and…
We study the wave equation on a bounded domain of $\mathbb R^m$ and on a compact Riemannian manifold $M$ with boundary. We assume that the coefficients of the wave equation are unknown but that we are given the hyperbolic…
Wave-like partial differential equations occur in many engineering applications. Here the engineering setup is embedded into the Hilbert space framework of functional analysis of modern mathematical physics. The notion wave-like is a…
We derive dispersion estimates for solutions of a one-dimensional discrete Dirac equations with a potential. In particular, we improve our previous result, weakening the conditions on the potential. To this end we also provide new results…
We investigate the behavior of the solutions of the ray equation in isotropic media. We discuss local and global transversals and wavefronts and give examples of rays without wavefronts.
A surface in a Riemannian space is called of constant astigmatism if the difference between the principal radii of curvatures at each point is a constant function. In this paper we give a classification of all rotational surfaces of…
Kernel matrices are a key quantity in kernel-based approximation, and important properties such as stability and algorithmic convergence can be analyzed with their help. In this work we refine a multivariate Ingham-type theorem, which is…
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
We construct an explicit solution of the Cauchy initial value problem for certain diffusion-type equations with variable coefficients on the entire real line. The corresponding Green function (heat kernel) is given in terms of elementary…
Using the elementary axioms of special relativity and quantum mechanics we construct a wave equation which generalizes the Schrodinger equation. We also solve the general second and some higher order differential equations.
It is well known that tau functions of the KP hierarchy satisfy addition formulas. We consider the general addition formula in the determinant form and take a certain limit of it. It expresses certain shifts of a tau function in terms of…