Blow-up of positive solutions for the semilinear heat equation with a potential

References

• Quittner P, Souplet P. Superlinear parabolic problems. Blow-up, global existence and steady states. 2nd ed. Verlag, Basel: Birkhäuser; 2019.
   Google Scholar
• Ishii H. Asymptotic stability and blowing up of solutions of some nonlinear equations. J Differ Equ. 1977;26(2):291–319.
   Web of Science ®Google Scholar
• Liu Y, Xu R, Yu T. Global existence, nonexistence and asymptotic behavior of solutions for the Cauchy problem of semilinear heat equations. Nonlinear Anal. 2008;68(11):3332–3348.
   Web of Science ®Google Scholar
• Weissler F. Existence and nonexistence of global solutions for a semilinear heat equation. Israel J Math. 1981;38(1-2):29–40.
   Web of Science ®Google Scholar
• Cheng T, Zheng G. Some blow-up problems for a semilinear parabolic equation with a potential. J Differ Equ. 2008;244(4):766–802.
   Web of Science ®Google Scholar
• Hamz MA, Zaag H. The blow-up rate for a non-scaling invariant semilinear heat equation. Arch Ration Mech Anal. 2022;244(1):87–125.
   Web of Science ®Google Scholar
• Mizoguchi N, Souplet P. Optimal condition for blow-up of the critical Lq norm for the semilinear heat equation. Adv Math. 2019;355:Article ID 106763.
   Web of Science ®Google Scholar
• Fujita H. On the blowing up of solutions of the Cauchy problem for ut=Δu+u1+α. J Fac Sci Univ Tokyo Sect I. 1966;13:109–124.
   Web of Science ®Google Scholar
• Giga Y, Matsui S, Sasayama S. Blow up rate for semilinear heat equations with subcritical nonlinearity. Indiana Univ Math J. 2004;53(2):483–514.
   Web of Science ®Google Scholar
• Kavian O. Remarks on the large time behaviour of a nonlinear diffusion equation. Ann Inst H Poincaré Anal Non Linéaire. 1987;4(5):423–452.
   Web of Science ®Google Scholar
• Lee T, Ni W. Global existence, large time behavior and life span of solutions of a semilinear parabolic Cauchy problem. Trans Amer Math Soc. 1992;333(1):365–378.
   Web of Science ®Google Scholar
• Levine HA. Some nonexistence and instability theorems for solutions of formally parabolic equations of the form Put=−Au+f(u). Arch Rational Mech Anal. 1973;51(5):371–386.
   Web of Science ®Google Scholar
• Zhang QS. Semilinear parabolic problems on manifolds and applications to the non-compact Yamabe problem. Electron J Differ Equ. 2000;46:1–30.
   Google Scholar
• Souplet P, Zhang Q. Stability for semilinear parabolic equations with decaying potentials in Rn and dynamical approach to the existence of ground states. Ann Inst H Poincaré Anal Non Linéaire. 2002;19(5):683–703.
   Web of Science ®Google Scholar
• Jleli M, Samet B, Souplet P. Discontinuous critical Fujita exponents for the heat equation with combined nonlinearities. Proc Amer Math Soc. 2020;148(6):2579–2593.
   Web of Science ®Google Scholar
• Li F, Liu J. Asymptotic results and critical Fujita exponent in parabolic equations with nonlocal nonlinearity. Appl Anal. 2022;101(18):6411–6434.
   Web of Science ®Google Scholar
• Yang C, Ji F, Yin Q. Fujita phenomenon in higher-order parabolic equation with nonlocal term. Appl Anal. 2018;97(6):1042–1048.
   Web of Science ®Google Scholar
• Giga Y, Kohn RV. Characterizing blowup using similarity variables. Indiana Univ Math J. 1987;36(1):1–40.
   Web of Science ®Google Scholar
• Galaktionov VA, Vázquez JL. The problem of blow-up in nonlinear parabolic equations. Amer Inst Math Sci. 2002;8(2):399–433.
   Google Scholar
• Matano H, Merle F. On nonexistence of type II blowup for a supercritical nonlinear heat equation. Comm Pure Appl Math. 2004;57(11):1494–1541.
   Web of Science ®Google Scholar
• Gidas B, Spruck J. Global and local behavior of positive solutions of nonlinear elliptic equations. Comm Pure Appl Math. 1981;34(4):525–598.
   Web of Science ®Google Scholar
• Giga Y. A bound for global solutions of semilinear heat equations. Comm Math Phys. 1986;103(3):415–421.
   Web of Science ®Google Scholar
• Gross L. Logarithmic Sobolev inequalities. Amer J Math. 1975;97(4):1061–1083.
   Web of Science ®Google Scholar
• Herrero MA, Velázquez JJL. Blow-up behaviour of one-dimensional semilinear parabolic equations. Ann Inst H Poincaré Anal Non Linéaire. 1993;10(2):131–189.
   Web of Science ®Google Scholar
• Andreucci D, Herrero MA, Velázquez JJL. Liouville theorems and blow up behaviour in semilinear reaction diffusion systems. Ann Inst H Poincaré Anal Non Linéaire. 1997;14(1):1–53.
   Web of Science ®Google Scholar