Critical exponents and blow-up rate for a nonlinear diffusion equation with logarithmic boundary flux

In this paper, we establish the critical global existence exponent and the critical Fujita exponent for the nonlinear diffusion equation ut=(logσ(1+u)ux)xut=(logσ(1+u)ux)x, in R+×(0,+∞)R+×(0,+∞), subject to a logarithmic boundary flux −logσ(1+u)ux(0,t)=(1+u)logp(1+u)(0,t),t∈(0,+∞), furthermore give the blow-up rate for the nonglobal solutions.