Existence and Nonexistence of Global Solutions of the Quasilinear Parabolic Equations with Inhomogeneous Terms. (18th October 2010) - Kobayashi, Yasumaro
Abstract : We consider the quasilinear parabolic equation with inhomogeneous termu t = Δ u m + 〈 x 〉 σ u p + f ( x ), u ( x, 0 ) = u 0 ( x ), where0 ≤ f ( x ), u 0 ( x ) ∈ C ( ℝ N ), m > 0, p > max { 1, m }, andσ > − 2, 〈 x 〉 : = ( | x | 2 + 1 ) 1 / 2 . In this paper, we investigate the critical exponents of this equation.