On a parabolic strongly nonlinear problem on manifolds

In this work we will prove the existence uniqueness and asymptotic behavior of weak solutions for the system (*) involving the pseudo Laplacian operator and the condition $\displaystyle\frac{\partial u}{\partial t} + \sum_{i=1}^n \big|\frac{\partial u}{\partial x_i}\big|^{p-2}\frac{\partial u}{\partial x_i}\nu_i + |u|^{\rho}u=f$ on $\Sigma_1$, where $\Sigma_1$ is part of the lateral boundary of the cylinder $Q=\Omega \times (0,T)$ and $f$ is a given function defined on $\Sigma_1$

An Ontological Approach to Inform HMI Designs for Minimizing Driver Distractions with ADAS

ADAS (Advanced Driver Assistance Systems) are in-vehicle systems designed to enhance driving safety and efficiency as well as comfort for drivers in the driving process. Recent studies have noticed that when Human Machine Interface (HMI) is not designed properly, an ADAS can cause distraction which would affect its usage and even lead to safety issues. Current understanding of these issues is limited to the context-dependent nature of such systems. This paper reports the development of a holistic conceptualisation of how drivers interact with ADAS and how such interaction could lead to potential distraction. This is done taking an ontological approach to contextualise the potential distraction, driving tasks and user interactions centred on the use of ADAS. Example scenarios are also given to demonstrate how the developed ontology can be used to deduce rules for identifying distraction from ADAS and informing future designs

On a parabolic strongly nonlinear problem on manifolds

El libro de María Valero se propone realizar una aproximación crítica a la presencia de unidades fraseológicas en la gramática y en la lexicografía, tarea ardua y compleja que la autora lleva a cabo con sumo cuidado y competencia metodológica

Weak solutions for a strongly-coupled nonlinear system

In this paper the authors study the existence of local weak solutions of the strongly nonlinear system u″ + Au + ƒ(u, v)u = h1 v″ + Av + g(u, v)v = h2 where A is the pseudo-Laplacian operator and ƒ, g, h1 and h2 are given functions.Mathematic

Nonlinear perturbations of the Kirchhoff equation

In this article we study the existence and uniqueness of local solutions for the initial-boundary value problem for the Kirchhoff equation u″ - M(t, ∥u(t)∥2)∆u + |u|ρ = ƒ in Ω x (0, T0), u = 0 on Γ0 x]0, T0[, ∂u/∂v + δh(u′) = 0 on Γ1 x]0, T0[, where Ω is a bounded domain of ℝn with its boundary consisting of two disjoint parts Γ0 and Γ1; ρ > 1 is a real number; v(x) is the exterior unit normal vector at x ∈ Γ1 and δ(x), h(s) are real functions defined in Γ1 and ℝ, respectively. Our result is obtained using the Galerkin method with a special basis, the Tartar argument, the compactness approach, and a Fixed-Point method.Mathematic

Nonlinear perturbations of the Kirchhoff equation

In this article we study the existence and uniqueness of local solutions for the initial-boundary value problem for the Kirchhoff equation \displaylines{ u'' - M(t,\|u(t)\|^{2})\Delta u + |u|^{\rho} =f \quad\text{in } \Omega \times (0, T_0), \cr u=0\quad\text{on }\Gamma_0 \times ]0, T_0[, \cr \frac{\partial u}{\partial \nu} + \delta h(u')=0 \quad\text{on } \Gamma_1 \times ]0, T_0[, } where $\Omega$ is a bounded domain of $\mathbb{R}^n$ with its boundary constiting of two disjoint parts $\Gamma_0$ and $\Gamma_1$; $\rho >1$ is a real number; $\nu(x)$ is the exterior unit normal vector at $x \in \Gamma_1$ and $\delta(x), h(s)$ are real functions defined in $\Gamma_1$ and $\mathbb{R}$, respectively. Our result is obtained using the Galerkin method with a special basis, the Tartar argument, the compactness approach, and a Fixed-Point method

Weak solutions for a strongly-coupled nonlinear system

In this paper the authors study the existence of local weak solutions of the strongly nonlinear system $$displaylines{ u''+mathcal{A}u +f(u,v)u = h_1 cr v''+mathcal{A}v +g(u,v)v = h_2 }$$ where $mathcal{A}$ is the pseudo-Laplacian operator and $f$, $g$, $h_1$ and $h_2$ are given functions

Global solutions to a quasilinear hyperbolic equation

This article concerns the existence and decay of solutions of a mixed problem for a quasilinear hyperbolic equation which has its motivation in a mathematical model that describes the nonlinear vibrations of the cross-section of a bar.Mathematic