In this paper, we consider singular and degenerate parabolic equations$$u_t =(x^alpha u_x)_x +u^m (x_0,t)v^{n} (x_0,t),quadv_t =(x^beta v_x)_x +u^q (x_0,t)v^{p} (x_0,t),$$ in $(0,a)times (0,T)$, subject to nullDirichlet boundary conditions, where $m,n, p,qge 0$, $alpha, betain [0,2)$ and $x_0in (0,a)$. The optimal classification of non-simultaneous and simultaneous blow-up solutions is determin...

The aim of this paper is to refine some results concerning the blow-up of solutions of the exponential reaction-diffusion equation. We consider solutions that blow-up in finite time, but continue to exist as weak solutions beyond the blow-up time. The main result is that these solutions become regular immediately after the blow-up time. This result improves on that of Fila, Matano and Polácik, ...

We consider the blow-up of solutions for a semilinear reaction diffusion equation with exponential reaction term. It is know that certain solutions that can be continued beyond the blow-up time possess a nonconstant selfsimilar blow-up profile. Our aim is to find the final time blow-up profile for such solutions. The proof is based on general ideas using semigroup estimates. The same approach w...

We obtain some sufficient conditions under which solutions to a nonlinear parabolic equation of second order with nonlinear boundary conditions tend to zero or blow up in a finite time. We also give the asymptotic behavior of solutions which tend to zero as t→ ∞. Finally, we obtain the asymptotic behavior near the blow-up time of certain blow-up solutions and describe their blow-up set.

Historically, the concern of wind instrumentalists has been diaphragm control and embouchure. Laryngeal movement during "blow" has been overlooked or neglected by wind musicians. It has been said that musical tone has to be produced by the resonances of the player's air column by opening his larynx during blow. In the present study, fiberscopic observations of the larynx during blow revealed th...

BACKGROUND Pollination has a great effect on the yield of fruit trees. Blow flies are considered as an effective pollinator compared to hand pollination in fruit orchards. Therefore, this study was designed to evaluate the effect of different pollination methods in mango orchards. METHODOLOGY The impact of pollination on quantity and quality of mango yield by blow flies was estimated by using...

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.