Abstract We describe the small-time heat kernel asymptotics of real powers $\operatorname {\Delta }^r$ , $r \in (0,1)$ a non-negative self-adjoint generalized Laplacian }$ acting on sections Hermitian vector bundle $\mathcal {E}$ over closed oriented manifold M . First, we treat separately asymptotic diagonal $M \times M$ and in compact set away from it. Logarithmic terms appear only if n is od...

Radial blow-up, including inhomogeneous versions, of boundary faces of a manifold (always with corners) is an important tool for resolving singularities, degeneracies and competing notions of homogeneity. These constructions are shown to be particular cases of generalized boundary blow-up in which a new manifold and blow-down map are constructed from, and conversely determine, combinatorial dat...

Self-similar blow-up behaviour for the fourth-order quasilinear p-Laplacian equation with source, ut = −(|uxx| uxx)xx + |u| u in R × R+, where n > 0, p > 1, is studied. Using variational setting for p = n+1 and branching techniques for p 6= n+1, finite and countable families of blow-up patterns of the self-similar form uS(x, t) = (T − t) − 1 p−1 f(y), where y = x/(T − t) , β = − p−(n+1) 2(n+2)(...

The course aims at presenting an introduction to the subject of singularity formation in nonlinear evolution problems usually known as blowup. In short, we are interested in the situation where, starting from a smooth initial configuration, and after a first period of classical evolution, the solution (or in some cases its derivatives) becomes infinite in finite time due to the cumulative effec...

The structure of the blow-up in nite time of a solution of the Generalized Korteweg-de Vries equation arising from a perturbed unstable solitary wave is studied numerically. The computed solution is observed to blow-up in the L 1-norm in nite time by forming a spike of innnite height at x = x and at t = t. Scaled coordinates are introduced to examine the detailed structure of the solution in th...

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Blow-up criteria of smooth solutions for the 3D micropolar fluid equations are investigated. Logarithmically improved blow-up criteria are established in the Morrey-Campanto space.

We prove here the existence of boundary blow up solutions for fully nonlinear equations in general domains, for a nonlinearity satisfying KellerOsserman type condition. If moreover the nonlinearity is non decreasing , we prove uniqueness for boundary blow up solutions on balls for operators related to Pucci’s operators.

In this paper, we give a symplectic proof for Seiberg-Witten blow-up formula of four dimensional symplectic manifolds, especially we interpret a strange phenomenon that the genera of embedding J-holomorphic curves will decrease when we symplectically blow-up the four dimensional symplectic manifold.

We use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the generalized KP-BBM equation. A number of explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain periodic wave solutions, kink wave solutions, unbounded wave solutions, blow-up wave sol...

We evaluated the acute toxicities and the physiological effects of plant monoterpenoids (eugenol, pulegone, citronellal and alpha-terpineol) and neuroactive insecticides (malathion, dieldrin and RH3421) on flight muscle impulses (FMI) and wing beat signals (WBS) of the blow fly (Phaenicia sericata). Topically-applied eugenol, pulegone, citronellal, and alpha-terpineol produced neurotoxic sympto...