Complicated asymptotic behavior exponents for solutions of the evolution p-Laplacian equation with absorption.

In this paper, we investigate how the initial value belonging to spaces $W_{\sigma}(\mathbb{R}^{N})$ ( $0<\sigma<N$ ) affects the complicated asymptotic behavior of solutions for the Cauchy problem of the evolution p-Laplacian equation with absorption. In fact, we reveal the fact that $\sigma=\frac{p}{q-p+1}$ is the critical exponent for the complicated asymptotic behavior of the solutions. [ABSTRACT FROM AUTHOR]