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The operator $L_{0} : D_{L_{0}} \subset H \to H$ , $L_{0} u = \frac{1}{r} \frac{d}{d r} \{r \frac{d}{d r} [\frac{1}{r} \frac{d}{d r} (r \frac{d u}{d r})]\}$ , $D_{L_{0}} = {u \in C^{4} ([0, R]), u^{'} (0) = u^{''''} (0) = 0, u (R) = u^{'} (R) = 0}$ , $H = L_{2, r} (0, R)$ is shown to be essentially self-adjoint, positive definite with a compact resolvent. The conditions on $L_{0}$ (in fact, on a general symmetric operator) are given so as to justify the application of the Fourier method for solving the problems of the types $L_{0} u = g$ and $u_{t t} + L_{0} u = g$ , respectively.

A study of bending waves in infinite and anisotropic plates

Ove Lindblom, Reinhold Näslund, Lars-Erik Persson, Karl-Evert Fällström (1997)

Applications of Mathematics

In this paper we present a unified approach to obtain integral representation formulas for describing the propagation of bending waves in infinite plates. The general anisotropic case is included and both new and well-known formulas are obtained in special cases (e.g. the classical Boussinesq formula). The formulas we have derived have been compared with experimental data and the coincidence is very good in all cases.

Active optimal control of the KdV equation using the variational iteration method.

Kucuk, Ismail (2010)

Mathematical Problems in Engineering

Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.

Muro, Masakazu (2004)

Journal of Lie Theory

Almansi decompositions for polyharmonic, polyheat, and polywave functions

Guangbin Ren, Uwe Kähler (2006)

Studia Mathematica

We construct Almansi decompositions for a class of differential operators, which include powers of the classical Laplace operator, heat operator, and wave operator. The decomposition is given in a constructive way.

An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics

A. Bourgeade, Ph. Le Floch, P. A. Raviart (1989)

Annales de l'I.H.P. Analyse non linéaire

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A Quadrature-Based Approach to Improving the Collocation Method.

A representation formula for the voltage perturbations caused by diametrically small conductivity inhomogeneities. Proof of uniform validity

A river water quality model for time varying BOD discharge concentration.

A rotation invariant differential equation for vector fields

A scaled characteristics method for the asymptotic solution of weakly nonlinear wave equations.

A sequential theory of some semigroups in special spaces of generalized functions

A study of an operator arising in the theory of circular plates

A study of bending waves in infinite and anisotropic plates

Active optimal control of the KdV equation using the variational iteration method.

Algorithmic construction of hyperfunction solutions to invariant differential equations on the space of real symmetric matrices.

Almansi decompositions for polyharmonic, polyheat, and polywave functions

Almost continuous solutions of geometric Hamilton–Jacobi equations

An analytical solution of the generalized equation of energy transport in one-dimensional semi-infinite domains.

An application of classical analysis.

An approximate analytic solution of a particular boundary value problem.

An asymptotic expansion for the discrete harmonic potential.

An asymptotic expansion for the solution of the generalized Riemann problem. Part 2 : application to the equations of gas dynamics

An asymptotic formula for the Green's function of an elliptic operator

An elastic Green matrix for a semistrip.

An explicit formula for symmetric polynomials related to the eigenfunctions of Calogero-Sutherland models.

Currently displaying 21 – 40 of 734