purpose: to determine the prevalence of intraocular injuries in patients with blow-out fracture and also to evaluate the etiologic mechanism of orbital blow-out fractures methods: this study is a consecutive case series analysis of 116 patients with orbital blow-out fractures. the patients were visited by an ophthalmologist within 24 hours of trauma. results: ninety-one men and twenty-five wome...

The equation ut = ∆u + u with homegeneous Dirichlet boundary conditions has solutions with blow-up if p > 1. An adaptive time-step procedure is given to reproduce the asymptotic behvior of the solutions in the numerical approximations. We prove that the numerical method reproduces the blow-up cases, the blow-up rate and the blow-up time. We also localize the numerical blow-up set.

introduction: fractures of the orbital floor, which are caused by various mechanisms, result in the herniation of periorbital tissue into the paranasal sinuses and its subsequent complications. early diagnosis using various techniques and reduction of fractures are necessary to preserve ocular function and esthetic. use of an endoscope has been associated with some advantages, including a decre...

This paper deals with blow-up properties of solutions to a semilinear parabolic system with nonlinear localized source involved a product with local terms ut = Δu+ exp{mu(x,t)+nv(x0 ,t)}, vt = Δv+ exp{pu(x0,t)+qv(x,t)} with homogeneous Dirichlet boundary conditions. We investigate the influence of localized sources and local terms on blow-up properties for this system, and prove that: (i) when ...

In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...

This thesis is concerned with the study of the Blow-up phenomena for parabolic problems, which can be defined in a basic way as the inability to continue the solutions up to or after a finite time, the so called blow-up time. Namely, we consider the blow-up location in space and its rate estimates, for special cases of the following types of problems: (i) Dirichlet problems for semilinear equat...

lim t→T ‖u(t)‖H 1 0 ( ) =+∞. A point a ∈ is called a blow-up point of u if there exists (an, tn) → (a,T ) such that |u(an, tn)| → +∞. The set of all blow-up points of u(t) is called the blow-up set and denoted by S. From Giga and Kohn [8, Theorem 5.3], there are no blow-up points in ∂ . Therefore, we see from (3) and the boundedness of that S is not empty. Many papers are concerned with the Cau...

We analyze the blow-up behavior of one-parameter collocation solutions for Hammerstein-type Volterra integral equations (VIEs) whose solutions may blow up in finite time. To approximate such solutions (and the corresponding blow-up time), we will introduce an adaptive stepsize strategy that guarantees the existence of collocation solutions whose blow-up behavior is the same as the one for the e...