Blowup solutions and their blowup rates for parabolic equations with non-standard growth conditions

This paper concerns classical solutions for homogeneous Dirichlet problem of parabolic equations coupled via exponential sources involving variable exponents. We first establish blowup criteria for positive solutions. And then, for radial solutions, we obtain optimal classification for simultaneous and non-simultaneous blowup, which is represented by using the maxima of the involved variable exponents. At last, all kinds of blowup rates are determined for both simultaneous and non-simultaneous blowup solutions. Mathematics Subject Classification (2000) : 35K55, 35B40, 35K15, 35B33.