Results 91 to 100 of about 18,029 (270)
On series of Walsh eigenfunctions [PDF]
Proceedings of the American Mathematical Society, 1951 and the boundary conditions u(O) = 0, u(1) = 0, the function g(x) being assumed continuous on 0 ? x < 1. He used the asymptotic formula for the kth eigenfunction (1) uk(x) = (2)1/2 [sin k7rx + (1/k)4k(x)], | k(X) | _ C. Comparing series of these functions with corresponding series of the functions (2) Uk(X) = (2)1/2 sin kirx, he proved that if a ...
openaire +2 more sources
Mathematical Methods in the Applied Sciences, Volume 48, Issue 8, Page 8793-8805, 30 May 2025.ABSTRACT We study a class of models for nonlinear acoustics, including the well‐known Westervelt and Kuznetsov equations, as well as a model of Rasmussen that can be seen as a thermodynamically consistent modification of the latter. Using linearization, energy estimates, and fixed‐point arguments, we establish the existence and uniqueness of solutions ...
Herbert Egger, Marvin Fritz
wiley +1 more source
On the Solution of Boundary Value Problems Set in Domains With Moving Boundaries
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We construct solutions for time‐dependent boundary value problems set in moving domains with Dirichlet, Neumann, and mixed boundary conditions. When the boundaries are time deformations of an initial boundary along a vector field, we can refer the boundary problem to a fixed domain at the cost of increasing the complexity of the coefficients ...
Ana Carpio, Gema Duro
wiley +1 more source
Spectral problem for the sixth order nonclassical differential equations
Қарағанды университетінің хабаршысы. Математика сериясы, 2020 In this article we investigate the correctness of boundary value problems for a sixth order quasi-hyperbolic equation in the Sobolev space Lu = −D6t u + ∆u − λu (Dt =∂/∂t , ∆ = Σni=1∂2/∂x2i – Laplace operator, λ – real parameter). For the given operator
A.I. Kozhanov +4 more
doaj +1 more source
The Eigenfunctions of the q-Harmonic Oscillator on the Quantum Line [PDF]
arXiv, 2004 We construct a complete set of eigenfunctions of the q-deformed harmonic oscillator on the quantum line. In particular the eigenfunctions corresponding to the non-Fock part of the spectrum will be constructed.
arxiv
Eigenfunction statistics for a point scatterer on a three-dimensional torus [PDF]
, 2012 In this paper we study eigenfunction statistics for a point scatterer (the Laplacian perturbed by a delta-potential) on a three-dimensional flat torus. The eigenfunctions of this operator are the eigenfunctions of the Laplacian which vanish at the scatterer, together with a set of new eigenfunctions (perturbed eigenfunctions).
arxiv +1 more source
The One‐Dimensional Coulomb Hamiltonian: Properties of Its Birman–Schwinger Operator
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT The objective of the present paper is to study in detail the properties of the Birman–Schwinger operator for a self‐adjoint realization of the one‐dimensional Hamiltonian with the Coulomb potential, both when the Hamiltonian is defined only on ℝ+$$ {\mathbb{R}}_{+} $$ and when it is defined on the whole real line.
S. Fassari +4 more
wiley +1 more source
Localized Eigenfunctions: Here You See Them, There You Don't [PDF]
arXiv, 2009 This expository note explores Laplacian eigenfunction localization for compact domains. We work in the context of a particular numerically determined, localized, low frequency eigenfunction.
arxiv
Mathematical Methods in the Applied Sciences, EarlyView.ABSTRACT We have studied possible applications of a particular pseudodifferential algebra in singular analysis for the construction of fundamental solutions and Green's functions of a certain class of elliptic partial differential operators. The pseudodifferential algebra considered in the present work, comprises degenerate partial differential ...
Heinz‐Jürgen Flad +1 more
wiley +1 more source
Biorthogonality condition for axisymmetric stokes flow in spherical geometries
International Journal of Mathematics and Mathematical Sciences, 2000 We derive the biorthogonality condition for axisymmetric Stokes flow in a region between two concentric spheres. This biorthogonality condition is a property satisfied by the eigenfunctions and adjoint eigenfunctions, which is needed to compute the ...
S. A. Khuri
doaj +1 more source