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非线性扩散方程：赵俊宁教授论文选
作者：赵俊宁 著
出版社：厦门大学出版社
出版时间：2021-11-01
ISBN：9787561583975
定价：¥128.00
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内容简介
本书为赵俊宁教授从事科研工作所发表的论文选集，内容包含拟线性退化抛物和椭圆方程的可解性问题、自由边界问题、解的渐进性质，以及Navier-Stokes方程的适定性理论研究成果；具体表现为利用BV估计技巧解决了一维具对流项的拟线性弱退化抛物方程有界可测解的唯一性问题，以及高维强退化拟线性抛物方程BV解的唯一性；将偏微分方程理论应用到对一般的渗流方程讨论源型奇异解的存在性和非存在性问题，为源型奇异解的研究提供了一个新的途径等。
作者简介
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目录
第一章 拟线性退化抛物方程的可解性
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.具非负特征形式的二阶拟线性方程第一边值问题.数学年刊，A辑，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 拟线性退化抛物方程解的性质
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
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.具非负特征形式的二阶拟线性方程第一边值问题.数学年刊，A辑，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 拟线性退化抛物方程解的性质
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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