A degenerate diffusion equation with a nonlinear source term

Nonlinear Analysis, Theory, Methods and Applications

Volumn 28, Issue 12, 1997, Pages 1977-1995

  Wiegner, Michael ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

Asymptotic behaviour; Blow up; Degenerate parabolic equations

Indexed keywords

ASYMPTOTIC STABILITY; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; DIFFUSION; MATHEMATICAL TRANSFORMATIONS;

ASYMPTOTIC BEHAVIOR; BLOW UP; CAUCHY PROBLEM; DEGENERATE DIFFUSION EQUATION;

NONLINEAR EQUATIONS;

EID: 0031168091     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0362-546X(96)00027-2     Document Type: Article

References (14)

1. CRANDALL, M. G., RABINOWITZ, P. H. and TARTAR L., On a Dirichlet problem with a singular nonlinearity. Comm. Part. Diff. Eqn, 1977, 2, 193-222.
2. DAL PASSO, R. and LUCKHAUS, S., A degenerate diffusion problem not in divergence form. J. Diff. Eqn, 1987, 69, 1-14.
3. FRIEDMAN, A. and McLEOD, B., Blow-up of solutions of nonlinear parabolic equations. Arch. Rat. Mech. Anal., 1986, 96, 55-80.
4. GATICA, J. A., OLIKER, V. and WALTMAN, P., Singular nonlinear boundary value problems for second-order ordinary differential equations. J. Diff. Eqn, 1989, 79, 62-78.
5. GILBARG, D. and TRUDINGER, N. S., Elliptic Partial Differential Equations of Second Order, 2nd edn. Springer, Berlin, 1983.
6. KAWOHL, B., On a Class of Singular Elliptic Equations, Progress in PDE: Elliptic and Parabolic Problems, ed. Bandle, Bemelmans et al. Pitman Research Notes in Math. 266, 1992, pp. 156-163.
7. LADYZHENSKAYA, O. A., URAL'TSEVA, N. N. and SOLONNIKOV, V. A., Linear and Quasilinear Equations of Parabolic Type. AMS, Providence, RI, 1968.
8. LAZER, A. C. and McKENNA, P. J., On a singular nonlinear elliptic boundary-value problem. Proc. AMS, 1991, 111, 721-730.
9. MATANO, H., Asymptotic Behavior and Stability of Solutions of Semilinear Diffusion Equations, Vol. 15. Publ. RIMS, Kyoto Univ., 1979, pp. 401-454.
10. MEIER, P., Explosion von Lösungen semilinearer parabolischer Differentialgleichungen. Dissertation, Basel, 1987.
11. SACKS, P. E., Global behavior for a class of nonlinear evolution equations. SIAM J. Math. Anal., 1985, 16, 233-250.
12. p. Indiana Univ. Math. J., 1980, 29, 79-102.
13. WIEGNER, M., Blow-up for solutions of some degenerate parabolic equations. Diff. and Int. Equations, 1994, 7(6), 1641-1647.
14. ZIMMER, T., On a degenerate parabolic equation. IWR Heidelberg, 1993, preprint, pp. 93-05.