In this paper we prove existence of global in time weak solutions for a highly nonlinear PDE system arising in the context of damage phenomena in thermoviscoelastic materials. The main novelty of the present contribution with respect to the ones already present in the literature consists in the possibility of taking into account a damage-dependent thermal expansion coefficient. This term implie...

1. Introduction. The purpose of this article is to study long time existence for high dimensional quasilinear wave equations exterior to star-shaped obstacles. In particular, we seek to prove exterior domain analogs of the four dimensional results of [5] where the nonlinearity is permitted to depend on the solution not just its first and second derivatives. Previous proofs in exterior domains o...

We prove that if u is a weak solution to a constant coefficient system (with strong ellipticity assumed along the horizontal direction) in a Carnot group (no restriction on the step), then u is actually smooth. We then use this result to develop blow-up analysis to prove a partial regularity result for weak solutions of certain non-linear systems.

We consider the free boundary problem for current-vortex sheets in ideal incompressible magnetohydrodynamics. The problem of current-vortex sheets arises naturally, for instance, in geophysics and astrophysics. We prove the existence of a unique solution to the constant-coefficient linearized problem and an a priori estimate with no loss of derivatives. This is a preliminary result to the study...

In this paper we consider the continuous–time nonlinear filtering problem, which has an infinite–dimensional solution in general, as proved by Chaleyat–Maurel and Michel. There are few examples of nonlinear systems for which the optimal filter is finite dimensional, in particular Kalman’s, Beneš’, and Daum’s filters. In the present paper, we construct new classes of scalar nonlinear filtering p...

In this paper we consider the continuous–time nonlinear filtering problem, which has an infinite–dimensional solution in general, as proved by Chaleyat–Maurel and Michel. There are few examples of nonlinear systems for which the optimal filter is finite dimensional, in particular Kalman’s, Beneš’, and Daum’s filters. In the present paper, we construct new classes of scalar nonlinear filtering p...

This paper introduces the Global-Local Mapping Approximation algorithm as a candidate for identifying nonlinear, six degree-of-freedom rigid body aircraft dynamics. The technique models the nonlinear dynamical model as a sum of linear model and nonlinear model. The linear model dynamics are assumed to be perturbed by a nonlinear term which represents the system nonlinearities that are not captu...

Tracking a ballistic missile in its reentry phase is one of the missile defence challenges as these reentry vehicles penetrate with large aerodynamic loads and sudden decelerations from exoatmospheric to endoatmospheric phase. With the advent of anti-ballistic missiles, the main goal of missile defence systems is to track the reentry vehicle to locate them precisely for allowing midair altitude...

In this article, a time dependent partial differential equation is used to model the nonlinear boundary value problem describing heat transfer through a radial porous moving fin with rectangular profile. The study is performed by applying a numerical solver in MATLAB (pdepe), which is a centered finite difference scheme. The thermal conductivity and fin surface emissivity are linearly ...

The Treatment Effect, the Cross Difference, and the Interaction Term in Nonlinear “Difference-in-Differences” Models I demonstrate that Ai and Norton’s (2003) point about cross differences is not relevant for the estimation of the treatment effect in nonlinear “difference-in-differences” models such as probit, logit or tobit, because the cross difference is not equal to the treatment effect, wh...