Lifespan estimates of solutions to semilinear wave equations with damping term on the exterior domain

References

• Strauss WA. Nonlinear scattering theory at low energy. J Funct Anal. 1981;41:110–133.
   Web of Science ®Google Scholar
• John F. Blow-up of solutions of nonlinear wave equations in three space dimensions. Manuscr Math. 1979;28:235–268.
   Web of Science ®Google Scholar
• Kitamura S, Morisawa K, Takamura H. The lifespan of classical solutions of semilinear wave equations with spatial weights and compactly supported data in one space dimension. J Differ Equ. 2022;307:486–516.
   Web of Science ®Google Scholar
• Lai NA, Liu MY, Wakasa K, et al. Lifespan estimates for 2 dimensional semilinear wave equations in asymptotically Euclidean exterior domains. J Funct Anal. 2021;281:109253.
   Google Scholar
• Lai NA, Zhou Y. Blow-up for initial boundary value problem of critical semilinear wave equation in two space dimensions. Commun Pure Appl Math. 2018;17:1499–1510.
   Google Scholar
• Lin YH, Lai NA, Ming S. Lifespan estimate for semilinear wave equation in Schwarzschild spacetime. Appl Math Lett. 2020;99:105997.
   Web of Science ®Google Scholar
• Wakasa K, Yordanov B. Blow-up of solutions to critical semilinear wave equations with variable coefficients. J Differ Equ. 2019;266:5360–5376.
   Web of Science ®Google Scholar
• Zhou Y. Blow up of classical solutions to ◻u=|u|1+α in three space dimensions. J Partial Differ Equ. 1992;5:21–32.
   Google Scholar
• Zhou Y, Han W. Blow-up of solutions to semilinear wave equations with variable coefficients and boundary. J Math Anal Appl. 2011;374:585–601.
   Web of Science ®Google Scholar
• Zhou Y, Han W. Lifespan of solutions to critical semilinear wave equations. Commun Partial Differ Equ. 2014;39(3):439–451.
   Web of Science ®Google Scholar
• Lai NA, Zhou Y. An elementary proof of Strauss conjecture. J Funct Anal. 2014;267(5):1364–1381.
   Web of Science ®Google Scholar
• Zhou Y. Cauchy problem for semilinear wave equations in four space dimensions with small initial data. J Differ Equ. 1995;8:135–144.
   Google Scholar
• Wirth J. Solution representations for a wave equation with weak dissipation. Math Methods Appl Sci. 2004;27:101–124.
   Web of Science ®Google Scholar
• Wirth J. Wave equations with time dependent dissipation. I. Non-effective dissipation. J Differ Equ. 2006;222:487–514.
   Web of Science ®Google Scholar
• Wirth J. Wave equations with time dependent dissipation. II. Effective dissipation. J Differ Equ. 2007;232:74–103.
   Web of Science ®Google Scholar
• Fujiwara K, Ikeda M, Wakasugi Y. Estimates of lifespan and blow-up rate for the wave equation with a time dependent damping and a power type nonlinearity. Funkc Ekvacioj. 2019;62:157–189.
   Web of Science ®Google Scholar
• Ikeda M, Sobajima M, Wakasugi Y. Sharp lifespan estimates of blow-up solutions to semilinear wave equations with time dependent effective damping. J Hyperbolic Differ Equ. 2019;16(3):495–517.
   Web of Science ®Google Scholar
• Lai NA, Zhou Y. The sharp lifespan estimate for semilinear damped wave equation with Fujita critical power in high dimensions. J Math Pure Appl. 2019;123:229–243.
   Web of Science ®Google Scholar
• Ikeda M, Wakasugi Y. Global well-posedness for the semilinear damped wave equation with time dependent damping in the overdamping case. Proc Am Math Soc. 2020;148(1):157–172.
   Web of Science ®Google Scholar
• Dao TA. A result for non-existence of global solutions to semilinear structural damped wave model. Preprint 2019. Available from: arXiv:1912.07066v1.
   Google Scholar
• Georgiev V, Palmieri A. Critical exponent of Fujita type for the semilinear damped wave equation on the Heisenberg group with power nonlinearity. J Differ Equ. 2020;269:420–448.
   Web of Science ®Google Scholar
• Ikeda M, Ogawa T. Lifespan of solutions to the damped wave equation with a critical nonlinearity. J Differ Equ. 2016;261:1880–1903.
   Web of Science ®Google Scholar
• Ikeda M, Sobajima M. Sharp upper bound for lifespan of solutions to some critical semilinear parabolic, dispersive and hyperbolic equations via a test function method. Nonlinear Anal. 2019;182:57–74.
   Web of Science ®Google Scholar
• Lai NA, Takamura H, Wakasa K. Blow-up for semilinear wave equations with the scale invariant damping and super Fujita exponent. J Differ Equ. 2017;263(9):5377–5394.
   Web of Science ®Google Scholar
• Lai NA, Takamura H. Blow-up for semilinear damped wave equations with sub-critical exponent in the scattering case. Nonlinear Anal. 2018;168:222–237.
   Web of Science ®Google Scholar
• Li HY, Li XT, Yan WP. Lifespan of solutions to semilinear damping wave equations in de Sitter spacetime. Nonlinear Anal. 2020;195:111735.
   Google Scholar
• Wakasa K, Yordanov B. On the non-existence of global solutions for critical semilinear wave equations with damping in the scattering case. Nonlinear Anal. 2019;180:67–74.
   Web of Science ®Google Scholar
• Imai T, Kato M, Takamura H, et al. The lifespan of solutions of semilinear wave equations with the scale invariant damping in two space dimensions. J Differ Equ. 2020;269:8387–8424.
   Web of Science ®Google Scholar
• Lai NA, Takamura H. Non-existence of global solutions of nonlinear wave equations with weak time dependent damping related to Glassey's conjecture. Differ Integral Equ. 2019;32(1–2):37–48.
   Web of Science ®Google Scholar
• Lai NA, Tu ZH. Strauss exponent for semilinear wave equations with scattering space dependent damping. J Math Anal Appl. 2020;489:124189.
   Google Scholar
• Dao TA, Fino AZ. Critical exponent for semilinear structurally damped wave equation of derivative type. Preprint 2020. Available from: arXiv:2004.08486v2.
   Google Scholar
• Hamouda M, Hamaz MA. Blow-up for wave equation with the scale invariant damping and combined nonlinearities. Preprint 2020. Available from: arXiv:2006.12600v1.
   Google Scholar
• Hidano K, Wang CB, Yokoyama K. Combined effects of two nonlinearities in lifespan of small solutions to semilinear wave equations. Math Ann. 2016;366:667–694.
   Web of Science ®Google Scholar
• Lai NA, Takamura H. Non-existence of global solutions of wave equations with weak time dependent damping and combined nonlinearity. Nonlinear Anal Real World Appl. 2019;45:83–96.
   Web of Science ®Google Scholar
• Liu MY, Wang CB. Blow-up for small amplitude semilinear wave equations with mixed nonlinearities on asymptotically Euclidean manifolds. J Differ Equ. 2020;269:8573–8596.
   Web of Science ®Google Scholar
• Chen WH, Palmieri A. Weakly coupled system of semilinear wave equations with distinct scale invariant terms in the linear part. Z Angew Math Phys. 2019;67:1–21.
   Google Scholar
• Dao TA, Reissig M. The interplay of critical regularity of nonlinearities in a weakly coupled system of semilinear damped wave equations. J Differ Equ. 2021;299:1–32.
   Web of Science ®Google Scholar
• Hao JH, Du FQ. Decay and blow-up for a viscoelastic wave equation of variable coefficients with logarithmic nonlinearity. J Math Anal Appl. 2022;506:125608.
   Google Scholar
• Ikeda M, Jleli M, Samet B. On the existence and non-existence of global solutions for certain semilinear exterior problems with nontrivial Robin boundary conditions. J Differ Equ. 2020;269:563–594.
   Web of Science ®Google Scholar
• Ikeda M, Tanaka T, Wakasa K. Critical exponent for the wave equation with a time dependent scale invariant damping and a cubic convolution. J Differ Equ. 2021;270:916–946.
   Web of Science ®Google Scholar
• Ming S, Lai SY, Fan XM. Lifespan estimates of solutions to quasilinear wave equations with scattering damping. J Math Anal Appl. 2020:492(1):124441.
   Google Scholar
• Ming S, Lai SY, Fan XM. Blow-up for a coupled system of semilinear wave equations with scattering dampings and combined nonlinearities. Appl Anal. 2020. doi:10.1080/00036811.2020.1834086
   Web of Science ®Google Scholar
• Ming S, Yang H, Fan XM. Blow-up and lifespan estimates of solutions to the weakly coupled system of semilinear Moore–Gibson–Thompson equations. Math Methods Appl Sci. 2021;44:10972–10992.
   Google Scholar
• Ming S, Yang H, Fan XM, et al. Blow-up and lifespan estimates of solutions to semilinear Moore–Gibson–Thompson equations. Nonlinear Anal Real World Appl. 2021;62:103360.
   Google Scholar
• Palmieri A, Takamura H. Non-existence of global solutions for a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case. Preprint 2018. Available from: arXiv:1812.10653v1.
   Google Scholar
• Palmieri A, Takamura H. Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities. Nonlinear Anal. 2019;187:467–492.
   Web of Science ®Google Scholar
• Palmieri A, Takamura H. Non-existence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear terms. Preprint 2019. Available from: arxiv:1901.04038.
   Google Scholar
• Sobajima M, Wakasa K. Finite time blow-up of solutions to semilinear wave equation in an exterior domain. J Math Anal Appl. 2019;48:123667.
   Google Scholar
• Zha DB. Global stability of solutions to two dimension and one dimension systems of semilinear wave equations. J Funct Anal. 2022;282:109219.
   Google Scholar