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.

Abstract In this paper we give a sharper sufficient condition for blow-up of the solution to nonlinear Schrödinger equation with free/Stark/quadratic potential by improving well known Zakharov–Glassey’s method.

We consider the critical nonlinear Schrödinger equation iut = −∆u − |u| 4 N u with initial condition u(0, x) = u0 in dimension N . For u0 ∈ H1, local existence in time of solutions on an interval [0, T ) is known, and there exists finite time blow up solutions, that is u0 such that limt→T<+∞ |ux(t)|L2 = +∞. This is the smallest power in the nonlinearity for which blow up occurs, and is critical...

Many audio and multimedia applications would benefit from the ability to classify and search for audio based on its characteristics. The audio analysis, search, and classification engine described here reduces sounds to perceptual and acoustical features. This lets users search or retrieve sounds by any one feature or a combination of them, by specifying previously learned classes based on thes...

where u and φ1, φ2 are, respectively, the complexand the real-valued functions of spatial coordinates x, y and the time t. The parameters σ, κ, γ,m1,m2, λ, n are real constants and σ is normalized as | σ |= 1. The GDS system has been derived to model 2 + 1 dimensional wave propagation in a bulk medium composed of an elastic material with couple stresses [1]. The parametric relation (λ − 1)(m2 −...