This paper deals with a class of localized and degenerate quasilinear parabolic systems ut = f (u)( u+ av(x0, t)), vt = g(v)( v + bu(x0, t)) with homogeneous Dirichlet boundary conditions. Local existence of positive classical solutions is proven by using the method of regularization. Global existence and blow-up criteria are also obtained. Moreover, the authors prove that under certain conditi...

In this paper, we’ll prove a L-concentration result of Zakharov system in space dimension two, with radial initial data (u0, n0, n1) ∈ Hs × L ×H−1 ( 17 < s < 1), when blow up of the solution happens by I-method. In additional to that we find a blow up character of this system. Furthermore, we improve the global existence result of Bourgain’s to above spaces.

In order to investigate the single-beam vertical beam-size blow-up observed[1] in the KEKB 3.5 GeV positron ring (LER), we performed beam-size observations using a highspeed gated camera capable of recording the image of a single bunch in the ring. Using this technique, we measured the beam-size dependence on bunch position along a train, and studied the onset of blow-up under various condition...

Bershadsky, Cecotti, Ooguri and Vafa constructed a real-valued invariant for Calabi–Yau manifolds, which is now called the BCOV invariant. In this paper, we extend to such pairs $(X,D)$ , where $X$ compact Kähler manifold $D$ pluricanonical divisor on with simple normal crossing support. We also study behavior of extended under blow-ups. The results in paper lead joint work Fu proving that bira...

The HIV/AIDS epidemic has many serious consequences for children. These consequences are, however, rarely inevitable. Families can provide a protective barrier that deflects blows, or minimises their impact and a supportive nurturing environment that can help children recover from harm. If strong enough, and with sufficient access to quality services and support from communities, families can r...

Abstract. In this paper, the author proposes a numerical method to solve a parabolic system of two quasilinear equations of nonlinear heat conduction with sources. The solution of this system may blow up in finite time. It is proved that the numerical solution also may blow up in finite time and an estimate of this time is obtained. The convergence of the scheme is obtained for particular value...

We study di erent notions of blow-up of a scheme X along a subscheme Y , depending on the datum of an embedding of X into an ambient scheme. The two extremes in this theory are the ordinary blow-up, corresponding to the identity, and the `quasi-symmetric blow-up', corresponding to the embedding of X into a nonsingular variety. We prove that this latter blow-up is intrinsic of Y and X , and is u...

Weobtain a hypergraph generalisation of the graph blow-up lemma proved byKomlós, Sarközy and Szemerédi, showing that hypergraphs with sufficient regularity and no atypical vertices behave as if they were complete for the purpose of embedding bounded degree hypergraphs. © 2011 Wiley Periodicals, Inc. Random Struct. Alg., 39, 275–376, 2011