Blow-up of solutions for the coupled wave equations featuring convolution nonlinearities

Abstract

Abstract: A class of Cauchy problem for coupled wave equations with convolutional nonlinear terms and scale invariant damping terms in n dimensional space was studied. By constructing the functionals andusing the iterative method, it is demonstrated that solutions to the small initial value problem in the sub-critical and critical cases will blow up at finite time. Furthermore, upper bound estimates for the lifespan of solutions is presented.

Key words: coupled wave equations, nonlinear convolution terms, iteration method, blow-up, lifespan estimates

CLC Number:

O175.29

QI Ming-ze, MING Sen, HAN Wei. Blow-up of solutions for the coupled wave equations featuring convolution nonlinearities[J]. Journal of Lanzhou University of Technology, 2026, 52(2): 151-157.

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: https://journal.lut.edu.cn/EN/

https://journal.lut.edu.cn/EN/Y2026/V52/I2/151

References

[1] LAI N A,TAKAMURA H.Blow-up for semilinear damped wave equations with subcritical exponent in the scattering case [J].Nonlinear Analysis,2018,168:222-237.
[2] LAI N A,TAKAMURA H.Nonexistence of global solutions of nonlinear wave equations with weaktime-dependent damping related to Glassey's conjecture [J].Differential and Integral Equations,2019,32(1/2):37-48.
[3] LAI N A,TAKAMURA H,WAKASA K.Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent [J].Journal of Differential Equations,2017,263(9):5377-5394.
[4] CHEN W H.Interplay effects on blow-up of weakly coupled systems for semilinear wave equations with general nonlinear memory terms [J].Nonlinear Analysis,2021,202:112160.
[5] PALMIERI A,TAKAMURA H.Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities [J].Nonlinear Analysis,2019,187:467-492.
[6] PALMIERI A,TAKAMURA H.Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations in the scattering case with mixed nonlinear terms [J].Nonlinear Differential Equations and Applications NoDEA,2019,27(6):58.
[7] PALMIERI A,TAKAMURA H.Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case [J].Mediterranean Journal of Mathematics,2020,17:13.
[8] FENG Z D,GUO F,LI Y Q.Blowup for a damped wave equation with mass and general nonlinear memory [J].Bulletin of the Malaysian Mathematical Sciences Society,2024,47(3):77.
[9] WAKASA K,YORDANOV B.On the nonexistence of global solutions for critical semilinear wave equations with damping in the scattering case [J].Nonlinear Analysis,2019,180:67-74.
[10] WAKASA K,YORDANOV B.Blow-up of solutions to critical semilinear wave equations with variable coefficients [J].Journal of Differential Equations,2019,266(9):5360-5376.
[11] ZHOU Y,HAN W.Blow-up of solutions to semilinear wave equations with variable coefficients and boundary [J].Journal of Mathematical Analysis and Applications,2011,374(2):585-601.
[12] PALMIERI A,TU Z.Lifespan of semilinear wave equation with scale invariant dissipation and mass and sub-Strauss power nonlinearity [J].Journal of Mathematical Analysis and Applications,2019,470(1):447-469.
[13] MING S,YANG H,FAN X M,et al.Blow-up and lifespan estimates of solutions to semilinear Moore-Gibson-Thompson equations [J].Nonlinear Analysis: Real World Applications,2021,62:103360.
[14] LAI N A,TAKAMURA H.Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity [J].Nonlinear Analysis: Real World Applications,2019,45:83-96.
[15] LAI N A,ZHOU Y.Blow-up and lifespan estimate to a nonlinear wave equation in Schwarzschild spacetime [J].Journal de Mathématiques Pures et Appliquées,2023,173:172-194.