This paper is devoted to the study of a nonlinear viscoelastic wave equation featuring a logarithmic feedback nonlinearity with a variable exponent m(.). We first prove the local and global well-posedness of solutions using the Galerkin approximation scheme, together with uniform a priori estimates and the Lions-Aubin compactness theorem. We then derive decay estimates by introducing a suitably designed Lyapunov functional.
We propose a methodology combining polynomial metamodeling and global optimization for estimating temperature and gas concentrations in propellant flames from moderate-resolution spectroradiometer measurements. We retrieve seven parameters: temperature, soot absorbance, concentrations of CO2 , H2O, CO, and HCl and the projected source area, and we estimate a Cram & eacute;r-Rao Lower Bound, which provides a reliable estimate of the minimal achievable error. We propose two sampling-based methods for optimization that give parameter estimation close to this bound. Our methodology is validated on representative synthetic cases and one experimental measurement, showing promising results for most parameters. A more complex retrieval method is discussed in the outlook section.
The alpha power Weibull distribution is a flexible generalization of the classical Weibull distribution that is capable of modeling a wide variety of data behaviors through its ability to accommodate multiple shapes of the hazard rate function. This flexibility makes it an attractive model for reliability and lifetime data analysis. Motivated by practical data collection constraints, this study investigates statistical inference for the alpha power Weibull distribution under the adaptive progressive Type-II censoring scheme. Classical estimation based on the maximum likelihood method is considered alongside Bayesian inference. In addition to the commonly used Metropolis-Hastings algorithm, this paper explores, for the first time, Bayesian estimation of the model parameters and associated reliability measures using the Hamiltonian Monte Carlo algorithm. Both point estimation and interval estimation are addressed, including asymptotic confidence intervals within the classical framework and highest posterior density credible intervals under the Bayesian approaches. The proposed methods are examined through a simulation study and an application to real data. The numerical results indicate that the Hamiltonian Monte Carlo algorithm provides more stable and efficient Bayesian inference under the adaptive progressive Type-II censoring plan when compared with the Metropolis-Hastings algorithm.
Inverse problems associated with thermal flow in porous media are typically ill-posed due to strong parameter heterogeneity, limited observations, and measurement noise. Efficient parameterizations and robust optimization strategies are therefore essential to ensure stable and computationally feasible reconstructions. In this work, we formulate the inversion of permeability fields as a PDE-constrained optimization problem, where space-dependent and partially observed parameters are represented through a conditional Karhunen-Lo & egrave;ve expansion (cKLE). The coefficients of the cKLE are treated as decision variables and are estimated by minimizing a nonlinear least-squares objective function that measures the mismatch between simulated and observed pressure and temperature data. To solve the resulting inverse problem, we employ deterministic optimization schemes based on the Levenberg-Marquardt (LM) method and Singular Value Decomposition (SVD). The use of cKLE enables an effective reduction of the parameter space while preserving the dominant spatial variability, significantly improving numerical stability and computational efficiency. The proposed methodology is evaluated using a field-scale thermal flow model based on Layer 10 of the SPE 10 benchmark, considering hot water injection under fixed-temperature boundary conditions. Numerical experiments with noise-free and noisy synthetic observations demonstrate that both LM and SVD schemes accurately reconstruct heterogeneous permeability fields, with robust performance under measurement uncertainty. The results highlight the effectiveness of combining dimensionality reduction with deterministic solvers for large-scale inverse problems in porous media.
The enhancement of railway infrastructure is increasingly important in meeting demand for heavier loads and higher-speed trains. Transition zones (e.g. bridges and culverts), where foundation properties change, are known to degrade more rapidly than standard track and so a comprehensive understanding of their mechanics is important. Available numerical methods capture complex geometries and behaviours however they are computationally intensive. It is of interest, therefore, to develop the availability of semi-analytical solutions for use in prototyping and comparison. The time-dependent response of an infinite Euler-Bernoulli beam on a piecewise-homogeneous viscoelastic foundation with a moving point load is currently without a published solution. We present a novel solution using the Laplace transform and the method of undetermined coefficients. The Laplace-domain solution is given analytically in terms of a linear system and is inverted numerically. We compare three representative inversion algorithms (direct quadrature, Weeks, and Gaver-Wynn rho). Weeks' method performs satisfactorily at low velocities and is advantageous if the solution is required at many times; however, it fails to converge for realistic velocities. The direct quadrature method gives reliable convergence at higher velocities despite Gibbs phenomena at small times. Gaver-Wynn rho consistently gives orders-of-magnitude better convergence with similar computation times.
