Critical Exponents of Fujita Type for Inhomogeneous Parabolic Equations and Systems

Journal of Mathematical Analysis and Applications

Volumn 251, Issue 2, 2000, Pages 624-648

  Bandle, C ^a   Levine, H A ^b   Zhang, Qi S ^c  

^a UNIVERSITY OF BASEL   (Switzerland)

^b IOWA STATE UNIVERSITY   (United States)

^c University of Memphis   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034668417     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jmaa.2000.7035     Document Type: Article

References (18)

1. Bandle C., Levine H. A. On the existence and nonexistence of global solutions of reaction-diffusion equations in sectorial domains. Text. Appl. Math. 655:1989;595-624.
2. Berestycki H., Dolcetta I. Capuzzo, Nirenberg L. Superlinear indefinite elliptic problems and nonlinear Liouville theorems. Topological Methods Nonlinear Anal. 4:1995;59-78.
3. Baras P., Pierre M. Critére d' existence de solutions positives pour des équations semi-linéaires non monotones. Ann. Inst. H. Poincaré, Analy. Non Linéaire. 2:1985;185-212.
4. Chen Z. Q., Williams R. J., Zhao Z. A Sobolev inequality and Neumann heat kernel estimate for unbounded domains. Math. Res. Lett. 1:1994;177-184.
5. Davies E. B. Heat Kernels and Spectral Theory. 1989;Camb. U. Press.
6. Deng K., Levine H. A. The role of critical exponents in blowup theorems, the sequel. J. Math. Anal. Appl. 243:2000;85-126.
7. Escobedo M., Herrero M. A. Boundedness and blow up for a semilinear reaction-diffusion equation. J. Differential Equations. 89:1991;176-202.
8. 1 + α. J. Fac. Sci. Univ. Tokyo, Sect. I. 13:1966;109-124.
9. Levine H. A. The role of critical exponents in blowup theorems. SIAM Rev. 32:1990;269-288.
10. Levine H. A., Zhang Q. S. The critical Fujita number for a semilinear heat equation in exterior domains with homogeneous Neumann boundary values. Proc. Royal Soc. Edinburgh, Sect. A. 130:2000;591-602.
11. Levine H. A. A Fujita type global existence-global nonexistence theorem for a weakly coupled system of reaction-diffusion equations. Z. Angew. Math. Phys. 42:1991;408-430.
12. Meier P. On the critical exponent for reaction-diffusion equations. Arch. Rational Mech. Anal. 109:1990;63-71.
13. Mizoguchi N., Yanagida E. Critical exponents for the blow-up of solutions with sign changes in a semilinear parabolic equation. Math. Ann. 307:1997;663-675.
14. d. J. Differential Equation. 133:1997;152-177.
15. n. Proc. Roy. Soc. Edinburgh Sect. A. 128:1998;123-136.
16. Zhang Q. S. A new critical phenomenon for semilinear parabolic problem. J. Math. Anal. Appl. 219:1998;123-139.
17. Zhang Q. S. Blow up and global existence of solutions to an inhomogeneous parabolic system. J. Differential Equations. 147:1998;155-183.
18. Zhang Q. S. Blow up results for nonlinear parabolic problems on manifolds. Duke Math. J. 97:1999;515-539.