References
- Birkner M. , Lopez-Mimbela J.A. and Wakolbinger A. Blow-up of semilinear PDE's at the critical dimension. A probabilistic approach . Proc. Amer. Soc. , 130 8 2431 – 2442 , 2002 . doi: Doi:10.1090/S0002-9939-02-06322-0 .
- Fino A. and Karch G. Decay of mass for nonlinear equation with fractional Laplacian . J. Monatsh. Math. , 160 : 375 – 384 , 2010 . doi: Doi:10.1007/s00605-009-0093-3 .
- Fujita , H. 1966 . On the blowing up of solutions of the cauchy problem for ut = Δu + u1 + α . J. Fac. Sci. Univ. Tokyo Sect. , 13 : 2431 – 2442 .
- Guedda M. and Kirane M. Criticality for some evolution equations . Differ. Eqs. , 37 : 540 – 550 , 2001 . doi: Doi:10.1023/A:1019283624558 .
- Hakem , A. 2005 . Blow-up results for evolution problems on ℝ n . Math. Nachr. , 278 ( 9 ) : 1 – 8 .
- Hayakawa K. On nonexistence of global solutions of some semilinear parabolic differential equations . Proc. Japan Acad. , 49 : 503 – 505 , 1973 . doi: Doi:10.3792/pja/1195519254 .
- Ju N. The maximum principle and the global attractor for the dissipative 2-D quasi-geostrophic equations . Comm. Pure. Appl. Anal. , pp. 161 – 181 , 2005 .
- Kilbas A.A. and Titioura A.A. Nonlinear differential equations with Marchaud-Hadamard type fractional derivative in the weighted space of summable functions . Math. Model. Anal. , 12 3 343 – 356 , 2007 . doi: Doi:10.3846/1392-6292.2007.12.343-356 .
- Kirane M. , Laskri Y. and N. E.-Tatar Critical exponents of Fujita type for certain evolution equtions and systems with spatio-temporal fractional derivatives . J. Math. Anal. Appl. , 312 2 488 – 501 , 2005 . doi: Doi:10.1016/j.jmaa.2005.03.054 .
- Kirane M. and Qafsaoui M. Global nonexistence for the cauchy problem of some nonlinear reaction-diffusion systems . J. Math. Anal. Appl. , 268 : 217 – 243 , 2002 . doi: Doi:10.1006/jmaa.2001.7819 .
- Kobayashi K. , Sirao T. and Tanaka H. On the blowing up problem for semilinear heat equations . J. Math. Soc. Japan , 29 : 407 – 424 , 1977 . doi: Doi:10.2969/jmsj/02930407 .
- Mitidieri , E. and Pokhozhaev , S.I. 2001 . A priori estimates and blow-up of solutions to nonlinear partial differential equations and inequalities . Proc. Steklov Inst. Math. , 234 : 1 – 383 .
- Podlubny , I. 1999 . Fractional Differential Equations , Vol. 198 , New-York, London : Math. Sci. Eng. Acad. Press .
- Pokhozhaev S.I. and Tesei A. A critical exponents for the absence of solutions for systems of quasilinear parabolic inequalities . Differ. Eqs. , 37 4 551 – 558 , 2001 . doi: Doi:10.1023/A:1019235708629 .
- Samko , S.G. , Kilbas , A.A. and Marichev , O.I. 1987 . Fractional Integrals and Derivatives, Theory and Applications , Gordon and Breach Sciences Publishers .
- Zhang Q.S. Blow-up results for nonlinear parabolic equations on manifolds . Duk. Math. J. , 97 : 515 – 593 , 1999 . doi: Doi:10.1215/S0012-7094-99-09719-3 .
- Zhang , Q.S. 2001 . Blow-up result for a nonlinear wave equation with damping, The critical case . C. R. Acad. Sci. Paris , 133 : 109 – 114 .