We determine the L p-L q-estimate of the linear equations of thermoelasticity for rhom-bic media in R 2. For this purpose we will transform the equations to an evolution equation showing that this equation has a unique solution with the help of the semigroup theory. In order to obtain the L p-L q-estimate, we will first apply the Fourier transformation to the evolution equation, thus determinin...

A parameter estimation problem is considered for a diagonaliazable stochastic evolution equation using a finite number of the Fourier coefficients of the solution. The equation is driven by additive noise that is white in space and fractional in time with the Hurst parameter H ≥ 1/2. The objective is to study asymptotic properties of the maximum likelihood estimator as the number of the Fourier...

in this article, vibration analysis of an euler-bernoulli beam resting on a pasternak-type foundation is studied. the governing equation is solved by using a spectral finite element model (sfem). the solution involves calculating wave and time responses of the beam. the fast fourier transform function is used for temporal discretization of the governing partial differential equation into a set ...

A computationally efficient numerical method is developed to investigate nonlinear interactions between steep surface gravity waves and depth-varying ocean currents. The free-surface boundary conditions are used to derive a coupled set of equations that are integrated in time for the evolution of the free-surface elevation and tangential component of the fluid velocity at the free surface. The ...

The time-dependent Schrödinger equationmodels the quantumnature ofmolecular processes. Numerical simulations of these models help in understanding and predicting the outcome of chemical reactions. In this thesis, several numerical algorithms for evolving the Schrödinger equation with an explicitly time-dependent Hamiltonian are studied and their performance is compared for the example of a pump...

We study the effect of Gaussian perturbations on a hyperbolic partial differential equation with double characteristics in two spatial dimensions. The coefficients our operator depend polynomially space variables, while noise is additive, white time and coloured space. provide sufficient condition spectral measure covariance functional describing that allows for existence random field solution ...

Quantum group Fourier transform methods are applied to the study of processes on noncommutative Minkowski spacetime [x, t] = ıλx. A natural wave equation is derived and the associated phenomena of in vacuo dispersion are discussed. Assuming the deformation scale λ is of the order of the Planck length one finds that the dispersion effects are large enough to be tested in experimental investigati...

A sharp regularity theory is established for homogeneous Gaussian fields on the unit circle. Two types of characterizations for such a field to have a given almost-sure uniform modulus of continuity are established in a general setting. The first characterization relates the modulus to the field’s canonical metric; the full force of Fernique’s zero-one laws and Talagrand’s theory of majorizing ...

Abstract. Time-harmonic oscillations of a horizontal plate generate internal gravity waves in an unbounded stratified fluid. A plane-wave (Fourier) decomposition is used in which waves with outgoing group velocity are selected. The pressure and the velocity in the far field are estimated in terms of the Fourier transform of the pressure jump across the plate. Explicit solutions are obtained for...