The temperature of a combustible material will rise or even blow up when a heat source moves across it. In this paper, we study the blow-up phenomenon in this kind of moving heat source problems in two-dimensions. First, a two-dimensional heat equation with a nonlinear source term is introduced to model the problem. The nonlinear source is localized around a circle which is allowed to move. By ...

Abstract Solutions to nonlinear Schrödinger equations may blow up in finite time. We study the influence of the introduction of a potential on this phenomenon. For a linear potential (Stark effect), the blow-up time remains unchanged, but the location of the collapse is altered. The main part of our study concerns isotropic quadratic potentials. We show that the usual (confining) harmonic poten...

In this paper, we study the solution of an initial boundary value problem for a quasilinear parabolic equation with a nonlinear boundary condition. We first show that any positive solution blows up in finite time. For a monotone solution, we have either the single blow-up point on the boundary, or blow-up on the whole domain, depending on the parameter range. Then, in the single blow-up point c...

We construct blow-up solutions of the energy critical wave map equation on R → N with polynomial blow-up rate (t for blow-up at t = 0) in the case when N is a surface of revolution. Here we extend the blow-up range found by Carstea (ν > 1 2 ) based on the work by Krieger, Schlag and Tataru to ν > 0. This work relies on and generalizes the recent result of Krieger and the author where the target...

Blow out fracture of orbit involves fracture of orbital floor without fracture of infraorbital rim. This injury is common from frontal blow to orbit. Frontal blow to orbit causes increased intraorbital tension causing fracture of floor of the orbit (weak point) with prolapse of orbital content into the maxillary sinus cavity. This causes enophthalmos and diplopia. Infraorbital rim is not involv...

Blow-up behaviour for the fourth-order quasilinear porous medium equation with source, (0.1) ut = −(|u|u)xxxx + |u|u in R × R+, n > 0, p > 1, is studied. Countable and finite families of similarity blow-up patterns of the form uS(x, t) = (T − t)− 1 p−1 f(y), where y = x/(T − t) , β = p−(n+1) 4(p−1) , which blow-up as t → T− < ∞, are described. These solutions explain key features of regional (f...

The tight transverse emittance budget for the LHC beam imposes severe constraints on the blow-up produced by injection errors. The modifications to the beam distributions and their possible parameterisation in terms of blow-up factors are discussed for betatron and dispersion mismatch as well as for injection offsets. The cases of initial uniform or gaussian distributions are considered in deta...

Determining the time of colonization of human or other animal remains by blow flies (Diptera: Calliphoridae) can play an important role in criminal investigations. However, blow fly presence in a given area is strongly influenced by abiotic and biotic variables such as temperature and habitat. We wanted to assess the biodiversity of adult blow flies in New Jersey, USA, where very little is know...

In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on some convergence of the perturbations for times smaller than the blow-up time of the unperturbed problem together with uniform bounds on the blow-up rates of the perturbed problems. We also present several examples. Among the...