Global Existence and Nonexistence Theorems for Quasilinear Evolution Equations of Formally Parabolic Type

Journal of Differential Equations

Volumn 142, Issue 1, 1998, Pages 212-229

  Levine, Howard A ^a   Park, Sang Ro ^a   Serrin, James ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001423038     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1997.3362     Document Type: Article

References (16)

1. Ball J. Remarks on blow-up and nonexistence theorems for nonlinear evolution equations. Quart. J. Math. Oxford (2). 28:1977;473-486.
2. Fila M. Boundedness of global solutions of nonlinear diffusion equations. J. Differential Equations. 98:1992;226-240.
3. Friedman A., McLeod B. Blow-up of positive solutions of semilinear heat equations. Indiana Univ. Math. J. 34:1985;425-447.
4. β. Differentsial 'nye Uravneniya. 17:1981;836-842.
5. Georgiev V., Todorova G. Existence of a solution of the wave equation with nonlinear damping and source terms. J. Differential Equations. 109:1994;295-308.
6. Kaplan S. On the growth of solutions of quasilinear parabolic equations. Comm. Pure Appl. Math. 16:1957;305-330.
7. Imai T., Mochizuki M. On blow-up of solutions for quasilinear degenerate parabolic equations. Publ. Res. Inst. Math. Sci. 27:1991;695-709.
8. Lacey A. A., Tzanetis D. Complete blow-up for a semilinear diffusion equation with a sufficiently large initial condition. IMA J. Appl. Math. 41:1988;207-215.
9. t=[Auu. Arch. Rational Mech. Anal. 51:1973;371-386.
10. Levine H. A. The role of critical exponents in blow-up theorems. SIAM Rev. 32:1990;262-288.
11. Levine H. A. Nonexistence of global solutions of nonlinear wave equations. Proceedings of N.S.F. Regional Conference on Improperly Posed Problems in Partial Differential Equations. Pitman Research Notes in Mathematics. 1:1975;Longman Sci. Math. Harlow. p. 95-104.
12. Levine H. A., Pucci P., Serrin J. Some remarks on global nonexistence for nonautonomous abstract evolution equations. Contemp. Math. 208:1997;253-263.
13. Levine H. A., Serrin J. Global nonexistence theorems for quasilinear evolution equations with dissipation. Arch. Rational Mech. Anal. 137:1997;341-361.
14. Nakao M. Asymptotic stability for some nonlinear evolution equation of second order with unbounded dissipative terms. J. Differential Equations. 30:1978;54-63.
15. Pucci P., Serrin J. Asymptotic stability for non-autonomous wave systems. Comm. Pure Appl. Math. 49:1996;177-216.
16. Samarskii A., Galaktionov V., Kurdyumov S., Mikhailov A. Blow-up in quasilinear parabolic equations. 1995;De Gruyter, Berlin.