EuDML | Browse

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.

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

Kucuk, Ismail (2010)

Mathematical Problems in Engineering

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.

Displaying 1 – 15 of 15

A decomposition method for a semilinear boundary value problem with a quadratic nonlinearity.

A note on Chebyshev series solution of the Crank-Gupta equation.

A Picard-Maclaurin theorem for initial value PDEs.

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

A rotation invariant differential equation for vector fields

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

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

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

Almansi decompositions for polyharmonic, polyheat, and polywave functions

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

An explicit solution of coupled viscous Burgers' equation by the decomposition method.

Analytical solution for the time-fractional telegraph equation.

Analytical treatment of generalized Burgers-Huxley equation by homotopy analysis method.

Application of decomposition to hyperbolic, parabolic, and elliptic partial differential equations.

Asymptotic behavior of solutions of the damped Boussinesq equation in two space dimensions.

Currently displaying 1 – 15 of 15