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- W2019977983 abstract "As a basic model, we study the 2mth-order quasilinear parabolic equation of diffusion-absorption type [Formula: see text] where Δ m,p is the 2mth-order p-Laplacian [Formula: see text]. We consider the Cauchy problem in R N × R + with arbitrary singular initial data u 0 ≠ 0 such that u 0 (x) = 0 for any x ≠ 0. We prove that, in the most delicate case p = q and [Formula: see text], this Cauchy problem admits the unique trivial solution u(·, t) = 0 for t > 0. For λ < λ 0 , such nontrivial very singular solutions are known to exist for some semilinear higher-order models. This extends the well-known result by Brezis and Friedman established in 1983 for the semilinear heat equation with p = q = m = 1." @default.
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- W2019977983 date "2006-06-01" @default.
- W2019977983 modified "2023-10-15" @default.
- W2019977983 title "HIGHER-ORDER QUASILINEAR PARABOLIC EQUATIONS WITH SINGULAR INITIAL DATA" @default.
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- W2019977983 doi "https://doi.org/10.1142/s0219199706002131" @default.
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