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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.

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