Existence and Nonexistence of Solutions for ut = div(|∇u|p - 2 ∇u) + f(∇u, u, x, t)

Journal of Mathematical Analysis and Applications

Volumn 172, Issue 1, 1993, Pages 130-146

  Junning, Zhao ^a  

^a JILIN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0011325358     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1006/jmaa.1993.1012     Document Type: Article

References (9)

1. N. D. Alikakos and L. C. Evans, Continuity of the gradient for weak solutions of a degenerate parabolic equation, J. Math. Anal. Appl. 63 (1983), 253-268.
2. J. Ball, Remarks on blowup and nonexistence theorems for nonlinear evolution equations, Quart. J. Math. Oxford 28 (1977). 473-486.
3. i = − Au + F(u), Arch. Rational Mech. Anal. 51 (1973), 371-386.
4. A. Friedman, "Partial Differential Equations of Parabolic Type," Prentice-Hall, Englewood Cliffs, NJ, 1964.
5. H. A. Levine and L. E. Payne, Nonexistence theorems for the heat equation with nonlinear boundary conditions and for the porous medium equation backward in time, J. Differential Equations 16 (1974), 319-334.
6. E. Coddington and N. Levinson, "Theory of Ordinary Differential Equations,” McGraw-Hill, New York, 1955.
7. E. DiBenedetto and A. Friedman, Holder estimates for nonlinear degenerate parabolic systems, J. Reine Angeif. Math. 357 (1985), 1 22.
8. Chen Yazhe, Holder continuity of the gradient of the solutions of certain degenerate parabolic equations, Chinese Ann. Math. Ser. B 8, No. 3 (1987), 343-356.
9. O. A. Ladyzfnskaja, V. A. Solonnikov. and N. N. Ural’ceva, "Linear and Quasilinear Equations of Parabolic Type,” Amer. Math. Soc., Providence, RI, 1968.