LAUSR

Abstract In this paper we give an existence theorem of global classical solution to the initial boundary value problem for the quasilinear parabolic equations of divergence form u t − div { σ ( | ∇ u | 2 ) ∇ u } = f ( ∇ u , u , x , t ) where σ ( | ∇ u | 2 ) may not be bounded as | ∇ u | → ∞ . As an application the logarithmic type nonlinearity σ ( | ∇ u | 2 ) = log ⁡ ( 1 + | ∇ u | 2 ) which is growing as | ∇ u | → ∞ and degenerate at | ∇ u | = 0 is considered under f ≡ 0 .