We consider the two dimensional L critical nonlinear Schrödinger equation i∂tu+ ∆u+ u|u| = 0. In the pioneering work [2], Bourgain and Wang have constructed smooth solutions which blow up in finite time T < +∞ with the pseudo conformal speed ‖∇u(t)‖L2 ∼ 1 T − t , and which display some decoupling between the regular and the singular part of the solution at blow up time. We prove that this dynam...

We study finite-time blow-up for pseudo-relativistic Hartreeand Hartree-Fock equations, which are model equations for the dynamical evolution of white dwarfs. In particular, we prove that radially symmetric initial configurations with negative energy lead to finite-time blow-up of solutions. Furthermore, we derive a mass concentration estimate for radial blow-up solutions. Both results are math...

For the carrion-feeding blow flies, a common source of vitellogenic protein are the carcasses that also serve as larval substrates. This attraction continues well after the blow flies have ceased to oviposit on the carrion, and it has been assumed that a decomposed cadaver remains a suitable source for vitellogenic protein; however, this assumption has never been tested. To test this hypothesis...

In 1961 Rossmann & Blow published a simple procedure for analytically combining the phase probabilities derived from various isomorphous derivatives or other phase-determining procedures [Rossmann & Blow (1961). Acta Cryst. 14, 641--647]. However, they found it necessary to make an approximation in obtaining the expression for the lack of closure (8) of the phase triangle. In 1970 Hendrickson &...

In the first part of the paper, we give an explicit algorithm to compute the (genus zero) Gromov-Witten invariants of blow-ups of an arbitrary convex projective variety in some points if one knows the Gromov-Witten invariants of the original variety. In the second part, we specialize to blow-ups of Pr and show that many invariants of these blow-ups can be interpreted as numbers of rational curv...

* Correspondence: [email protected] School of Automation, Southeast University, Nanjing 210096, China Full list of author information is available at the end of the article Abstract In this article, we investigate the Dirichlet problem for a porous medium equation with a more complicated source term. In some cases, we prove that the solutions have global blow-up and the rate of blow-up is unifo...

We establish blow-up profiles for any blowing-up sequence of solutions of general conformally invariant fully nonlinear elliptic equations on Euclidean domains. We prove that (i) the distance between blow-up points is bounded from below by a universal positive number, (ii) the solutions are very close to a single standard bubble in a universal positive distance around each blow-up point, and (i...

We use techniques from reaction-diffusion theory to study the blow-up and existence of solutions of the parabolic Monge–Ampère equation with power source, with the following basic 2D model (0.1) u t = −|D 2 u| + |u| p−1 u in R 2 × R + , where in two-dimensions |D 2 u| = u xx u yy − (u xy) 2 and p > 1 is a fixed exponent. For a class of " dominated concave " and compactly supported radial initia...

BACKGROUND Molecular tools are now widely used to address crucial management and conservation questions. To date, dart biopsying has been the most commonly used method for collecting genetic data from cetaceans; however, this method has some drawbacks. Dart biopsying is considered inappropriate for young animals and has recently come under scrutiny from ethical boards, conservationists, and the...

Abstract We consider a degenerate chemotaxis model with two-species and two-stimuli in dimension d ≥ 3 find two critical curves intersecting at one point which separate the global existence blow up of weak solutions to problem. More precisely, above these (i.e. subcritical case), problem admits solution obtained by limits strong an approximated system. Based on second moment solutions, initial ...