非线性扩散方程：赵俊宁教授论文选

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