in this paper, we investigate the application of the homotopy perturbation method (hpm) for solving a one-dimensional nonlinear inverse heat conduction problem. in this problem the thermal conductivity term is a linear function with respect to unknown heat temperature in bounded interval. furthermore, the temperature histories are unknown at the end point of the interval. this problem is ill-po...

Abstract. The process of recombination in population genetics, in its deterministic limit, leads to a nonlinear ODE in the Banach space of finite measures on a locally compact product space. It has an embedding into a larger family of nonlinear ODEs that permits a systematic analysis with lattice-theoretic methods for general partitions of finite sets. We discuss this type of system, reduce it ...

Einstein vacuum equations, that is a system of nonlinear partial differential equations (PDEs) are derived from Weyl metric by using relation between Einstein tensor and metric tensor. The symmetries of Einstein vacuum equations for static axisymmetric gravitational fields are obtained using the Lie classical method. We have examined the optimal system of vector fields which is further used to ...

This contribution concerns the problem of finite dimensional control for a class of systems described by nonlinear hyperbolic-parabolic coupled partial differential equations (PDE’s). Initially, Galerkin’s method is applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Af...

We present some sufficient conditions for the robustness of the unstable oscillations in nonlinear ODE with respect to the small hysteresis perturbations. MSC 2000: Primary: 34C55, Secondary: 34C25, 34D10 ∗This research was supported by the Enterprise Ireland, Grants SC/2000/138 and SC/2003/376.

Methodologies are presented for assessing the feasibility of parameter estimation in nonlinear ordinary di erential equation (ODE) models. These methods are applied to a recent model for hepatitis C viral dynamics. Subset selection is performed on themodel parameters, andmaximum likelihood estimation is conducted using available data from the literature.

This article presents a methodology for the synthesis of finite-dimensional nonlinear output feedback controllers for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. Initially, the nonlinear parabolic PDE system is expressed with respect to an appropriate time-invariant spatial coordinate, and a representative (with respect to different initi...