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• W2945305943 abstract "In this paper, we study an initial-boundary value problem for the following mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity in a bounded domain Ω⊂Rn:ut−Δut−div(|∇u|p−2∇u)=|u|q−2ulog⁡|u|,1<p≤q{<∞,if n≤p;<npn−p,if n>p, which is referred to as Showalter equation [1]. We focus on the initial conditions, which ensure the solutions of the model exist global, blow up in finite time and blow up at infinite time. Explicitly, we classify the ranges of p,q into two cases:(0.1)1<p≤q{≤2,if n≤p,≤2,if 2nn+2<p<n,<npn−p,if p≤2nn+2, and(0.2)1<p≤q and 2<q<{∞, if n≤p,npn−p, if 2nn+2<p<n. Let J(u0) be the initial energy (see (2.1) for the definition of J), I(u0) be the vale of Nehari functional at u0 (see (2.2) for the definition of I), d>0 be the mountain-pass level given in (2.4), and M∈[0,d] be the constant given in (2.6), we get If J(u0)≤d and I(u0)≥0, then the solution exists globally; If J(u0)≤d, I(u0)<0 and p,q satisfies (0.1), then the solution blows up at infinite time. Moreover, if in additionJ(u0){≤M, if M<d,<M, if M=d, the growth rate of the solution is got; If J(u0)≤M, I(u0)<0 and p,q satisfies (0.2), then the solution blows up in finite time." @default.
• W2945305943 created "2019-05-29" @default.
• W2945305943 creator A5043106122 @default.
• W2945305943 creator A5051491371 @default.
• W2945305943 date "2019-10-01" @default.
• W2945305943 modified "2023-10-11" @default.
• W2945305943 title "Global existence and blow-up for a mixed pseudo-parabolic p-Laplacian type equation with logarithmic nonlinearity" @default.
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• W2945305943 doi "https://doi.org/10.1016/j.jmaa.2019.05.018" @default.
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