Blow-Up of Solutions to the Fourth-Order Equation with Variable-Exponent Nonlinear Weak Damping

被引：4
|
作者：
Liao, Menglan [1 ]
Li, Qingwei [2 ]
机构：
[1] Hohai Univ, Coll Sci, Nanjing 210098, Peoples R China
[2] Dalian Maritime Univ, Sch Sci, Dalian 116026, Peoples R China
来源：
MEDITERRANEAN JOURNAL OF MATHEMATICS | 2023年 / 20卷 / 03期
关键词：
Fourth-order equations; nonlinear weak damping; variable-exponent nonlinearity; blow-up; the upper bound of the blow-up time; GLOBAL EXISTENCE; ASYMPTOTIC STABILITY; NONEXISTENCE;
D O I：
10.1007/s00009-023-02391-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this note, we investigate again the blow-up phenomenon of weak solutions to the following initial-boundary value problem of the fourth-order equation with variable-exponent nonlinearityu(tt) + ?(2)u - M(|| ?u ||(2))?u - ?u(t) + |ut|(m(x)-2)ut = |u|(p(x)-2)u.Our investigations reveal that the blow-up phenomenon will happen for arbitrarily high initial energy under m- := ess infx?O m(x) > 2. It is worthy to point out that an upper bound of the blow-up time is also shown. These results answer the earlier unsolved question in our previous paper (Liao and Tan in Sci China Math 66, 285-302 (2023).
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页数：16
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