We present adaptive procedures in space and time for the numerical study of positive solutions to the following problem,  ut(x, t) = (u)xx(x, t) (x, t) ∈ (0, 1)× [0, T ), (u)x(0, t) = 0 t ∈ [0, T ), (u)x(1, t) = u(1, t) t ∈ [0, T ), u(x, 0) = u0(x) x ∈ (0, 1), with p,m > 0. We describe how to perform adaptive methods in order to reproduce the exact asymptotic behavior (the blow-up rate an...

we discuss the asymptotic behaviour of solutions for the nonlocal quasilinear hyperbolic problem of kirchhoff type [ u_{tt}-phi (x)||nabla u(t)||^{2}delta u+delta u_{t}=|u|^{a}u,, x in mathbb{r}^{n} ,,tgeq 0;,]with initial conditions $u(x,0) = u_0 (x)$ and $u_t(x,0) = u_1 (x)$, in the case where $n geq 3, ; delta geq 0$ and $(phi (x))^{-1} =g (x)$  is a positive function lying in $l^{n/2}(mathb...

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...