We study attractive particle systems with stationary product measures. We utilize the property of attractivity and its link to coupling to build a growth process that samples from the stationary measure of the zero-range process, on fixed and finite lattices, with computation times scaling linearly with the number of particles N . The zero-range process with constant jump-rates and a single def...

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...

In this article, we present first a new technique to prove, in a general case, the recent result of Cazenave, Dickstein and Weissler [6] on the blowing-up solutions to a temporally nonlocal nonlinear parabolic equation. Then, we study the blow-up rate and the global existence in time of the solutions. Furthermore, we show necessary conditions for global existence.

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...

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 ...