【摘要】：本文主要研究具非線性對數源項和p-Laplace算子的拋物問題解的整體存在性與爆破性,即考慮如下問題首先給出預備知識和主要結果,其次利用位勢井方法以及能量估計,Sobolev嵌入不等式和反證法等證明解的整體存在性和解的正無窮時刻爆破性.具體講,根據初始能量和M=1/p2(p2e/n(?)p)n/p的大小關系以及I(u_0)=∫Ω|%絬_0|pdx-∫Ω|u_0|plog|u_0|dx的非負性,主要結論如下:定理1.若u_0(x)∈ W_0~(1,p)(Ω),J(u_0)M,I(u_0)≥ 0,則問題(0.1)有一個整體弱解u ∈ L~∞(0,+∞;w_0~(1,p)(Ω)),u,∈ L~2(0,+∞;L~2(Ω)).進一步,對所有t≥ 0,有如下估計定理2.若u_0(x)∈ W_0~(1,p)(Ω),J(u_0)= M,I(u_0)≥ 0,則問題(0.1)有一個整體弱解u ∈ L~∞(0,+∞;W_0~(1,p)(Ω)),u,∈ L~2(0,+∞;L~2(Ω)).進一步,若 I(u_0)0,對任意給定的正數γ,都存在t0,使得對所有Ω t,都有定理3.若 u_0(x)∈ W_0~(1,p)(Ω),J(u_0)≤ M,I(u_0)0,則問題(0.1)的解 u = u(x,t)在正無窮時刻爆破,且有
[Abstract]:In this paper, we mainly study the global existence and blow-up of solutions to parabolic problems with nonlinear logarithmic source terms and p-Laplace operators, that is, considering the following problems, we first give the preparatory knowledge and the main results, secondly, we use the potential well method and the energy estimation, Sobolev's embedding inequality and counterproof are used to prove the global existence of solutions and the blow-up of positive infinity time. Specifically, based on the relationship between the initial energy and M=1/p2 (p2e/n (?) p) n) and the nonnegativity of I (u?) =? 惟 |%) _ 0 | pdx-? 惟 | u? If u _ 0 (x) 鈭，

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