We present a mathematical characterization of hyperbolic gauge pathologies in electrodynamics and general relativity. We show analytically how non-linear gauge terms can produce a blow-up of some fields along characteristics. We expect similar phenomena to appear in any other gauge field theory. We also present numerical simulations where such blow-ups develop and show how they can be properly ...

A first order differential inequality technique is used on suitably defined auxiliary functions to determine lower bounds for blow-up time in initial-boundary value problems for parabolic equations of the form ut = div ( ρ(u)gradu )+ f (u) if blow-up occurs. In addition, conditions which ensure that blow-up occurs or does not occur are presented. © 2007 Elsevier Inc. All rights reserved.

First we give a truly short proof of the major blow up result [Si] on higher dimensional semilinear wave equations. Using this new method, we also establish blow up phenomenon for wave equations with a potential. This complements the recent interesting existence result by [GHK], where the blow up problem was left open.

This paper deals with a degenerate parabolic equation vt = ∆v + av1 ∥v∥1 α1 subject to homogeneous Dirichlet condition. The local existence of a nonnegative weak solution is given. The blow-up and global existence conditions of nonnegative solutions are obtained. Moreover, we establish the precise blow-up rate estimates for all the blow-up solutions.

Boundary value problems for non-linear parabolic equations with singular potentials are considered. Existence and non-existence results as an application of different Hardy inequalities proved. Blow-up conditions investigated too.

In the present work, we establish an optimal estimate for the electric potential difference between closely adjacent spherical perfect conductors in n dimensional space (n ≥ 2). This result indicates that electric fields blow up as a pair of spherical perfect conductors approach each other, and provides the lower bound with the optimal blowup rate which was recently established by Bao, Li and Y...

In the paper, several problems on the periodic Degasperis-Procesi equation with weak dissipation are investigated. At first, the local well-posedness of the equation is established by Kato’s theorem and a precise blow-up scenario of the solutions is given. Then, several criteria guaranteeing the blow-up of the solutions are presented. Moreover, the blow-up rate and blow-up set of the blowing-up...

Recently it was suggested that a graviton in AdS5 × S5 with a large momentum along the sphere can blow up into a spherical D-brane in S5. In this paper we show that the same graviton can also blow up into a spherical D-brane in AdS5 with exactly the same quantum numbers (angular momentum and energy). These branes are BPS, preserving 16 of the 32 supersymmetries. We show that there is a BPS clas...

We consider the 1D nonlinear Schrödinger equation (NLS) with focusing point nonlinearity, (0.1) i∂tψ + ∂ 2 xψ + δ|ψ|p−1ψ = 0, where δ = δ(x) is the delta function supported at the origin. In the L supercritical setting p > 3, we construct self-similar blow-up solutions belonging to the energy space Lx ∩Ḣ x. This is reduced to finding outgoing solutions of a certain stationary profile equation. ...