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

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 View the MathML source−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.