Blow-Up Phenomena for a Non-Homogeneously Strongly Damped Wave Equation with Riemann-Liouville Fractional Integral

XIANG Chang-yong, DUAN Ji-song, LONG Qun-fei

doi:10.13371/j.cnki.chin.q.j.m.2025.03.006

Chinese Quarterly Journal of Mathematics >

2025 , Vol. 40 >Issue 3: 304 - 312

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2025.03.006

Blow-Up Phenomena for a Non-Homogeneously Strongly Damped Wave Equation with Riemann-Liouville Fractional Integral

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School of Mathematics and Statistics, GuiZhou Normal University, Guiyang 550025, China

XIANG Chang-yong (1997-), male, native of Qianxi, Guizhou, graduate student of Guizhou Normal University, engages in partial differetial equation; DUAN Ji-song (2001-), male, native of Guiyang, Guizhou, graduate student of Guizhou Normal University, engages in partial differetial equation; LONG Qun-fei (1980-), male, native of Songtao, Guizhou, associate professor of Guizhou Normal University, engages in partial differetial equation.

XIANG Chang-yong (1997-), male, native of Qianxi, Guizhou, graduate student of Guizhou Normal University, engages in partial differetial equation

Received date: 2025-02-28

Online published: 2025-09-30

Supported by

Supported by National Natural Science Foundation of China (Grant No. 62363005).

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Abstract

We investigate the blow-up effect of solutions for a non-homogeneous wave equation
u_tt−∆u−∆u_t=I₀^α+ (|u|^p)+ω(x),
where p >1, 0≤α<1 and ω(x) with \int_{\mathbb{R}^{N}} ω(x)dx >0. By a way of combining the argument by contradiction with the test function techniques, we prove that not only any non-trivial solution blows up in finite time under 0< α <1, N ≥1 and p >1, but also any non-trivial solution blows up in finite time under α= 0, 2≤ N ≤4 and p being the Strauss exponent.

Key words： Finite time blow-up; Non-homogeneously strongly damped wave equation; Riemann-Liouville fractional integral; Strauss exponent

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XIANG Chang-yong, DUAN Ji-song, LONG Qun-fei . Blow-Up Phenomena for a Non-Homogeneously Strongly Damped Wave Equation with Riemann-Liouville Fractional Integral[J]. Chinese Quarterly Journal of Mathematics, 2025 , 40(3) : 304 -312 . DOI: 10.13371/j.cnki.chin.q.j.m.2025.03.006

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