We study the problem of the continuous dependence of weak and strong solutions to the initial boundary value problem for multidimensional marine riser equations on the parameters of the equation. The continuous dependence of solutions on the coefficient of the effective tension, on the coefficient of the nonlinear drag, and on the coefficients of the Coriolis force is established. © 2011 Elsevi...

A rigorous proof for existence and uniqueness of solutions to a class of singular nonlinear boundary value problems arising in viscous flow and heat transfer behind a shock wave is made and a theoretical estimate formula for the skin friction coefficient is presented. The formula can be successfully applied to estimate the value of the skin friction coefficient. The correctness of the analytica...

A nonlinear, Bayesian optimization scheme is presented for reconstructing fluorescent yield and lifetime, the absorption coefficient, and the diffusion coefficient in turbid media, such as biological tissue. The method utilizes measurements at both the excitation and the emission wavelengths to reconstruct all unknown parameters. The effectiveness of the reconstruction algorithm is demonstrated...

The nonlinear Diffuse Optical Tomography (DOT) problem involves the inversion of the associated coefficient-to-measurement operator, which maps the spatially varying optical coefficients of turbid medium to the boundary measurements. The inversion of the coefficient-to-measurement operator is approximated by using the Fréchet derivative of the operator. In this work, we first analyze the Born e...

An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient. The operator exponential is represented by a Dunford-Cauchy integral along a hyperbola enve...

In this work, a method for estimating the space-dependent perfusion coefficient parameter in a 2D bioheat transfer model is presented. In the method, the bioheat transfer model is transformed into a time-dependent semidiscrete system of ordinary differential equations involving perfusion coefficient values as parameters, and the estimation problem is solved through a nonlinear least squares tec...

An exponentially convergent approximation to the solution of a nonlinear first order differential equation with an operator coefficient in Banach space is proposed. The algorithm is based on an equivalent Volterra integral equation including the operator exponential generated by the operator coefficient. The operator exponential is represented by a Dunford-Cauchy integral along a hyperbola enve...

The structure algorithm provides an extension to nonlinear systems of the Kronecker canonical forms relative to linear constant-coefficient implicit differential systems. A connection with the index problem is sketched in the conclusion.

In this paper, we prove the existence of nontrivial nonnegative time periodic solutions for a pseudo-parabolic type equation with weakly nonlinear periodic sources. Moreover, we investigate the asymptotic behavior of solutions as the viscous coefficient k tends to zero.

By using the Lie’s invariance infinitesimal criterion we obtain the continuous equivalence transformations of a class of nonlinear Schrödinger equations with variable coefficients. Starting from the equivalence generators we construct the differential invariants of order one. We apply these latter ones to find the most general subclass of variable coefficient nonlinear Schrödinger equations whi...