The critical exponent for fast diffusion equation with nonlocal source

Fast Diffusion Equation with Critical Sobolev Exponent in a Ball

Rate of convergence to Barenblatt profiles for the fast diffusion equation with a critical exponent

We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation as t approaches the extinction time. We find a continuum of rates of convergence to a self-similar profile. These rates depend explicitly on the spatial decay rates of initial data.

Critical exponent of the fractional Langevin equation.

We investigate the dynamical phase diagram of the fractional Langevin equation and show that critical exponents mark dynamical transitions in the behavior of the system. For a free and harmonically bound particle the critical exponent alpha(c)=0.402+/-0.002 marks a transition to a nonmonotonic underdamped phase. The critical exponent alpha(R)=0.441... marks a transition to a resonance phase, wh...

A Nonlocal Convection-diffusion Equation

In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut = J ∗u−u+G ∗ (f(u))− f(u) in R, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equatio...

Critical Exponent for a Nonlinear Wave Equation with Damping

It is well known that if the damping is missing, the critical exponent for the nonlinear wave equation gu=|u| p is the positive root p0(n) of the equation (n&1) p&(n+1) p&2=0, where n 2 is the space dimension (for p0(1)= , see Sideris [14]). The proof of this fact, known as Strauss' conjecture [17], took more than 20 years of effort, beginning with Glassey doi:10.1006 jdeq.2000.3933, available ...