CRITICAL FUJITA EXPONENT FOR A FAST DIFFUSIVE EQUATION WITH VARIABLE COEFFICIENTS

Fast Diffusion Equation with Critical Sobolev Exponent in a Ball

Finite integration method with RBFs for solving time-fractional convection-diffusion equation with variable coefficients

In this paper, a modification of finite integration method (FIM) is combined with the radial basis function (RBF) method to solve a time-fractional convection-diffusion equation with variable coefficients. The FIM transforms partial differential equations into integral equations and this creates some constants of integration. Unlike the usual FIM, the proposed method computes constants of integ...

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 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 ...

Auxiliary equation method for the mKdV equation with variable coefficients

By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of nonlinear evolution equations with variable coefficients. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients. As a result, new explicit solutions including solitary wave solutions and trigonometric function solutions...