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非線(xiàn)性擴(kuò)散方程:趙俊寧教授論文選

非線(xiàn)性擴(kuò)散方程:趙俊寧教授論文選

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作 者: 趙俊寧 著
出版社: 廈門(mén)大學(xué)出版社
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標(biāo) 簽: 暫缺

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ISBN: 9787561583975 出版時(shí)間: 2021-11-01 包裝: 精裝
開(kāi)本: 16開(kāi) 頁(yè)數(shù): 665 字?jǐn)?shù):  

內(nèi)容簡(jiǎn)介

  本書(shū)為趙俊寧教授從事科研工作所發(fā)表的論文選集,內(nèi)容包含擬線(xiàn)性退化拋物和橢圓方程的可解性問(wèn)題、自由邊界問(wèn)題、解的漸進(jìn)性質(zhì),以及Navier-Stokes方程的適定性理論研究成果;具體表現(xiàn)為利用BV估計(jì)技巧解決了一維具對(duì)流項(xiàng)的擬線(xiàn)性弱退化拋物方程有界可測(cè)解的唯一性問(wèn)題,以及高維強(qiáng)退化擬線(xiàn)性?huà)佄锓匠藼V解的唯一性;將偏微分方程理論應(yīng)用到對(duì)一般的滲流方程討論源型奇異解的存在性和非存在性問(wèn)題,為源型奇異解的研究提供了一個(gè)新的途徑等。

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暫缺《非線(xiàn)性擴(kuò)散方程:趙俊寧教授論文選》作者簡(jiǎn)介

圖書(shū)目錄

第一章 擬線(xiàn)性退化拋物方程的可解性
1.The first boundary value problem for quasilinear degenerate parabolic equations of second order in several space variables. Chin. Ann. Math. Ser. B 4 (1983), no.1,57-76.(with Zhuoqun Wu)
2.Some general results on the first boundary value problem for quasilinear degenerate parabolic equations. Chin. Ann. Math. Ser. B 4 (1983), no. 3, 319-328. (withZhuoqun Wu)
3.具非負(fù)特征形式的二階擬線(xiàn)性方程第一邊值問(wèn)題.數(shù)學(xué)年刊,A輯,第4卷(1983),第4期、475-486
4.Uniqueness of solutions of quasilinear degenerate parabolic equations. Northeastern Math. J. 1 (1985), no. 2, 153-165
5.Applications of theory of compensated compactness to quasilinear degenerate parabolic equations and quasilinear degenerate elliptic equations. Northeastern Math. J.(1986), no. 1, 33-48
6.Source-type solutions of the porous media equation with absorption: the fast diffusion case. Nonlinear Anal. 14 (1990), no. 2, 107–121.(with Peletier L.A)
7.Source-type solutions of degenerate quasilinear parabolic equations. J. Differential Equations 92 (1991), no. 2, 179–198
8.Uniqueness of Solutions for Higher Dimensional Quasilinear Degenerate Parabolic Equation. Chin. Ann. Of Math. Ser. B 13 (1992), no. 2 129-136
Existence and Nonexistence of Solutions for u, = div (Vu)p-2Vu) + f(Vu, u, x, t). J Math. Anal. Appl. 172 (1993), no. 1, 130-146
10. Source-type solutions of a quasilinear degenerate parabolic equation with absorp-tion. Chin. Ann. Math. Ser. B 15 (1994), no.1, 89–104
11. Uniqueness of the solutions of u, = Au and u, = Au - uP when initial datum ameasures: the fast diffusion case, J. Partial Diff Eqs. 7 (1994), 143–159. (withHongjun Yuan)
12. On the Cauchy problem and initial traces for the evolution p-Laplacian equationswith strongly nonlinear sources. J. Differential Equations 121 (1995), no. 2,
13. Singular solutions for a convection diffusion equation with absorption. Acta Math Sci. 15 (1995), no. 4, 431-441
14. The Cauchy problem for u, = div(|Vu|p-2Vu) when 2N/(N + 1) ( p ( 2. NonlinearAnal. 24 (1995), no. 5, 615-630
15. The Cauchy problem and initial traces for a doubly nonlinear degenerate parabolic equa-tion. Sci. China Ser. A 39 (1996), no. 7, 673-684. (with Zhonghai Xu).
16. Uniqueness and stability of solutions for Cauchy problem of nonlinear diffusionequations. Sci. China Ser. A 40 (1997), no. 9, 917-925.(with Peidong Lei) .
17.On the Cauchy problem of evolution p-Laplacian equations with strongly nonlinear sources when 1 ( p ( 2. Acta Math. Sinica, Eng. Ser. 17(2001), no. 3, 455–470.(with Peidong Lei)
18.BV Solutions of Dirichlet Problem for a Class of Doubly Nonlinear Degenerate Parabolic Equations. J. Partial Diff. Eqs. 17 (2004), 241-254. (with Peigong Han) .
19.Uniqueness and stability of solution of Cauchy problem of degenerate quasilinearparabolic equations. Sci. China Ser. A 48 (2005), no. 5,583–593. (with HuashuiZhan)
20.Existence and uniqueness of renormalized solutions for a class of degenerate parabol-ic equations. Acta Math. Sci. Ser. B 29 (2009), no. 2, 251-264. (with Liqin Zhang)
21.On the Cauchy problem of evolution p-Laplacian equation with nonlinear gradientterm.Chin. Ann. Math. Ser. B 30 (2009), no. 1, 1–16. (with Mingyu Chen) .
22.The first boundary value problem for a class of quasilinear degenerate elliptic equa-tions. Acta Math. Sci. Ser. B 25 (2005),no.4,577–586. (with Xiaoming Zeng) . .
第二章 擬線(xiàn)性退化拋物方程解的性質(zhì)
1.Continuity of solutions for a class of quasilinear degenerate parabolic equations. Northeastern Math. J. 7 (1991), no. 3, 356-365
2.Some Properties of Solutions of Quasilinear Degenerate Parabolic Equations and Quasilinear Degenerate Elliptic Equations. Northeastern. Math. J. 2 (1986), no. 3,281-302.
3.Lipschitz continuity of solutions and interfaces of the evolution p-Laplacian equa-tion. Northeastern Math. J. 8 (1992), no. 1, 21-37.(with Hongjun Yuan)
4.The asymptotic behaviour of sol

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