Quasilinear parabolic and elliptic equations with nonlinear boundary conditions

C.V. Pao1
1Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, United States

Tài liệu tham khảo

Adams, 1981, On contracting interval iteration for nonlinear problems in Rn, Part II, Applications, Nonlinear Anal., 5, 525, 10.1016/0362-546X(81)90101-2 Ames, 1965 Anderson, 1995, Global existence for nonlinear diffusion equations, J. Math. Anal. Appl., 196, 479, 10.1006/jmaa.1995.1421 Aronson, 1981, Large time behavior of solutions of the porous medium equation in bounded domain, J. Differential Equations, 39, 378, 10.1016/0022-0396(81)90065-6 Bobisud, 1995, Existence of steady-state solutions for some one-dimensional conduction problems, J. Math. Anal. Appl., 195, 684, 10.1006/jmaa.1995.1383 Cannon, 1973, Determining unknown coefficients in a nonlinear heat conduction problem, SIAM J. Appl. Math., 24, 298, 10.1137/0124032 Cantrell, 1991, Diffusive logistic equations with indefinite weights: Population models in disrupted environments, II, SIAM J. Math. Anal., 22, 1043, 10.1137/0522068 Carl, 1996, Existence and monotone iterations for parabolic differential inclusions, Comm. Appl. Nonlinear Anal., 3, 1 Chen, 1989, Error estimates of optimal order for finite element methods with interpolated coefficients for nonlinear heat equation, IMA J. Numer. Anal., 9, 507, 10.1093/imanum/9.4.507 Delgado, 2002, On the structure of the positive solutions of the logistic equation with nonlinear diffusion, J. Math. Anal. Appl., 268, 200, 10.1006/jmaa.2001.7815 DiBenedetto, 1993 Frank-Kamenetskii, 1969 Galaktionov, 1995, On asymptotic self-similar behavior for a quasilinear heat equation: single point blow-up, SIAM J. Math. Anal., 26, 675, 10.1137/S0036141093223419 Hernández, 1998, Positive solutions for the logistic equation with unbounded weights, vol. 194, 183 Kwak, 2000, Mixed covolume methods for quasi-linear second-order elliptic problems, SIAM J. Numer. Anal., 38, 1057, 10.1137/S003614299935855X O.A. Ladyzenskaya, V.A. Solonnikov, N.N. Uralceva, Linear and Quasilinear Equations of Parabolic Type, Moscow, 1967 (English Transl. Amer. Math. Soc., Providence, RI, 1968) Leung, 1984, Nonlinear density-dependent diffusion for competing species interaction: Large-time asymptotic behavior, Proc. Edinburgh Math. Soci., 27, 131, 10.1017/S0013091500022227 Leung, 1990, Existence of positive solutions for elliptic systems—degenerate and nonhomogeneous ecological models, J. Math. Anal. Appl., 151, 512, 10.1016/0022-247X(90)90163-A Lieberman, 1996 Özisik, 1989 Özisik, 1994 Pao, 1992 Pao, 2005, Strongly coupled elliptic systems and application to Lotka–Volterra models with cross-diffusion, Nonlinear Anal., 60, 1197, 10.1016/j.na.2004.10.008 Pao, 1995, Finite difference reaction diffusion equations with nonlinear boundary conditions, Numer. Methods Partial Differential Equations, 11, 355, 10.1002/num.1690110405 Pao, 1980, Asymptotic behavior of solutions for a parabolic equation with nonlinear boundary conditions, Proc. Amer. Math. Soc., 80, 587, 10.1090/S0002-9939-1980-0587933-8 Schatzmann, 1984, Stationary solutions and asymptotic behavior of a quasilinear degenerate parabolic equation, Indiana Univ. Math. J., 33, 1, 10.1512/iumj.1984.33.33001 Sacks, 1983, Continuity of solutions of a singular parabolic equation, J. Nonlinear Anal., 7, 384, 10.1016/0362-546X(83)90092-5 Wang, 1998, Monotone method for diffusion equations with nonlinear coefficients, Nonlinear Anal., 34, 113, 10.1016/S0362-546X(97)00679-2 Wang, 2000, Finite difference reaction–diffusion equations with nonlinear diffusion coefficients, Numer. Math., 85, 485, 10.1007/s002110000140 Wang, 2002, Determination of an unknown coefficient in a nonlinear heat equation, J. Math. Anal. Appl., 271, 525, 10.1016/S0022-247X(02)00165-8