we devote to investigate the quenching phenomenon for a reaction-diffusion system with coupled singular absorption terms, ut Δu − u−p1v−q1 , vt Δv − u−p2v−q2 . The solutions of the system quenches in finite time for any initial data are obtained, and the blow-up of time derivatives at the quenching point is verified. Moreover, under appropriate hypotheses, the criteria to identify the simultane...

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...

Large eddy simulations of turbulent swirl-stabilised flames gradually approaching blow-off conditions in a gas turbine model combustor are undertaken. The global equivalence ratio the is reduced by increasing and decreasing air fuel flow rates respectively. filtered reaction rate for partially premixed combustion modelled using presumed joint probability density function flamelet model. average...

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...