Estimates on the blowup time for a quasilinear parabolic system

References

• Anderson JR, Deng K. Global existence for degenerate parabolic equations with a non-local forcing. Math. Meth. Appl. Sci. 1997;20:1069–1087.
   Web of Science ®Google Scholar
• Deng WB, Li YX, Xie CH. Blow-up and global existence for a nonlocal degenerate parabolic system. J. Math. Anal. Appl. 2003;277:199–217.
   Web of Science ®Google Scholar
• Du LL, Mu CL, Fan MS. Global existence and nonexistence for a quasilinear degenerate parabolic system with nonlocal source. Dyn. Syst. 2005;20:401–412.
   Web of Science ®Google Scholar
• Du LL. Blow-up for a degenerate reaction-diffusion system with nonlinear nonlocal sources. J. Comput. Appl. Math. 2007;202:237–247.
   Web of Science ®Google Scholar
• Duan ZW, Deng WB, Xie CH. Uniform blow-up profile for a degenerate parabolic system with nonlocal source. Comput. Math. Appl. 2004;47:977–995.
   Web of Science ®Google Scholar
• Li FC, Xie CH. Global existence and blow-up for a nonlinear porous medium equation. Appl. Math. Lett. 2003;16:185–192.
   Web of Science ®Google Scholar
• Bao AG, Song XF. Bounds for the blowup time of the solutions to quasi-linear parabolic problems. Z. Angew. Math. Phys.2014;65:115–123.
   Web of Science ®Google Scholar
• Liu BC, Li FJ. Properties of non-simultaneous blowup solutions in nonlocal parabolic equations. Nonlinear Anal. 2010;72:1065–1074.
   Web of Science ®Google Scholar
• Liu DM, Mu CL, Xin Q. Lower bounds estimate for the blow-up time of a nonlinear nonlocal porous medium equation, Acta Math. Sci. Ser. B Engl. Ed. 2012;32:1206–1212.
   Google Scholar
• Jumpen W, Sawangtong P. Lower and upper bounds for blow-up time in a degenerate semilinear parabolic problem. J. Math. Sci. Adv. Appl. 2010;5:209–219.
   Google Scholar
• Marras M. Bounds for blow-up time in nonlinear parabolic systems under various boundary conditions. Numer. Funct. Anal. Optim. 2011;32:453–468.
   Web of Science ®Google Scholar
• Payne LE, Philippin GA, Schaefer PW. Blow-up phenomena for some nonlinear parabolic problems. Nonlinear Anal. 2008;69:3495–3502.
   Web of Science ®Google Scholar
• Payne LE, Philippin GA, Schaefer PW. Bounds for blow-up time in nonlinear parabolic problems. J. Math. Anal. Appl. 2008;338:438–447.
   Web of Science ®Google Scholar
• Payne LE, Schaefer PW. Lower bounds for blow-up time in parabolic problems under Dirichlet conditions. J. Math. Anal. Appl. 2007;328:1196–1205.
   Web of Science ®Google Scholar
• Payne LE, Song JC. Lower bounds for the blow-up time in a nonliner parabolic problem. J. Math. Anal. Appl. 2009;354:394–396.
   Web of Science ®Google Scholar
• Schaefer PW. Lower bounds for blow-up time in some porous medium problems. Vol. 5, Dynamic systems and applications. Atlanta (GA): Dynamic; 2008. p. 442–445.
   Google Scholar
• Song JC. Lower bounds for the blow-up time in a non-local reaction-diffusion problem. Appl. Math. Lett. 2011;24:793–796.
   Web of Science ®Google Scholar
• Payne LE, Song JC. Lower bounds for blow-up in a model of chemotaxis. J. Math. Anal. Appl. 2012;385:672–676.
   Web of Science ®Google Scholar
• Xu XJ, Ye Z. Life span of solutions with large initial data for a class of coupled parabolic systems. Z. Angew. Math. Phys. 2013;64:705–717.
   Web of Science ®Google Scholar
• Bao AG, Song XF. Bounds for the blowup time of the solution to a parabolic system with nonlocal factors in nonlinearities. submitted for publication.
   Google Scholar
• Brändle C, Quirós F, Rossi JD. The role of non-linear diffusion in non-simultaneous blow-up. J. Math. Anal. Appl. 2005;308:92–104.
   Web of Science ®Google Scholar
• Espejo EE, Stevens A, Velázquez JJL. A note on non-simultaneous blow-up for a drift-diffusion model. Differ. Integr. Equ. 2010;23:451–462.
   Web of Science ®Google Scholar
• Li ZP, Mu CL, Du WJ. Non-simultaneous blow up for coupled nonlinear diffusion equations with absorptions. Z. Angew. Math. Phys. 2013;64:253–263.
   Web of Science ®Google Scholar
• Quirós F, Rossi JD. Non-simultaneous blow-up in a nonlinear parabolic system. Adv. Nonlinear Stud. 2003;3:397–418.
   Web of Science ®Google Scholar
• Rossi JD, Souplet P. Coexistence of simultaneous and nonsimultaneous blow-up in a semilinear parabolic system. Differ. Integr. Equ. 2005;18:405–418.
   Web of Science ®Google Scholar
• Talenti G. Best constant in Sobolev inequality. Ann. Mat. Pura Appl. 1976;110:353–372.
   Google Scholar