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...

* Correspondence: zhgs917@163. com Nonlinear Scientific Research Center, Faculty of Science, Jiangsu University, Zhenjiang 212013, China Full list of author information is available at the end of the article Abstract This article deals with the blow-up problems of the positive solutions to a nonlinear parabolic equation with nonlocal source and nonlocal boundary condition. The blow-up and globa...

We establish the existence of locally positive weak solutions to the homogeneous Dirichlet problem for ut = u∆u + u ∫ Ω |∇u| in bounded domains Ω ⊂ R which arises in game theory. We prove that solutions converge to 0 if the initial mass is small, whereas they undergo blow-up in finite time if the initial mass is large. In particular, it is shown that in this case the blow-up set coincides with ...

We present results for finite time blow-up for filtration problems with nonlinear reaction under appropriate assumptions on the nonlinearities and the initial data. In particular, we prove first finite time blow up of solutions subject to sufficiently large initial data provided that the reaction term ”overpowers” the nonlinear diffusion in a certain sense. Secondly, under related assumptions o...

We study in detail the blow-up procedure described in [BTW01]. We obtain a structure theorem for coreless polygroups as a double quotient space G/H, and a polygroup chunk theorem. Seeking to remove the arbitrary parameter needed for the blow-up, we find canonical ∅-invariant groupoids G > H analogous to G and H above, and show that H contains precisely all the arbitrary choices related to the b...

Stability of blow-up proole for equation of the type u t = u + juj p?1 u Abstract In this paper, we consider the following nonlinear equation u t = u + juj p?1 u u(:; 0) = u 0 ; (and various extensions of this equation, where the maximum principle do not apply). We rst describe precisely the behavior of a blow-up solution near blow-up time and point. We then show a stability result on this beha...

This work is concerned with positive classical solutions for a quasilinear parabolic equation with a gradient term and nonlinear boundary flux. We find sufficient conditions for the existence of global and blow-up solutions. Moreover, an upper bound for the ‘blow-up time’, an upper estimate of the ‘blow-up rate’ and an upper estimate of the global solution are given. Finally, some application e...

For a sequence of blow up solutions of the Yamabe equation on non-locally confonformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates of the Weyl tensor and its covariant derivatives at blow up points. If the Positive Mass Theorem held in dimensions 10 and 11, these estimates ...

We study blow-up rates and the blow-up profiles of possible asymptotically self-similar singularities of the 3D Euler equations, where the sense of convergence and self-similarity are considered in various sense. We extend much further, in particular, the previous nonexistence results of self-similar/asymptotically self-similar singularities obtained in [2, 3]. Some implications the notions for...

In this paper we analyze the asymptotic finite time blow-up of solutions to the heat equation with a nonlinear Neumann boundary flux in one space dimension. We perform a detailed examination of the nature of the blow-up, which can occur only at the boundary, and we provide tight upper and lower bounds for the blow-up rate for “arbitrary” nonlinear functions F , subject to very mild restrictions.