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Long-time dynamics of the parabolic $p$-Laplacian equation

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  • In this paper, we study the long-time behaviour of solutions of Cauchy problem for the parabolic $p$-Laplacian equation with variable coefficients. Under the mild conditions on the coefficient of the principal part and without upper growth restriction on the source function, we prove that this problem possesses a compact and invariant global attractor in $L^2(R^n)$.
    Mathematics Subject Classification: 35L55, 35B41.

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