A New Method for Blow-Up to Scale-Invariant Damped Wave Equations with Derivatives and Combined Nonlinear Terms

被引：1
作者：
Chen, Yuanming [1 ,2 ]
机构：
[1] Shanghai Univ Finance & Econ, Sch Econ, Shanghai 200433, Peoples R China
[2] Lishui Univ, Dept Math, Lishui 323000, Zhejiang, Peoples R China
来源：
SYMMETRY-BASEL | 2022年 / 14卷 / 02期
关键词：
blow-up; lifespan; damped wave equation; scale invariant; test function; GLOBAL EXISTENCE; LIFE-SPAN;
D O I：
10.3390/sym14020198
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The Cauchy problems of scale-invariant damped wave equations with derivative nonlinear terms and with combined nonlinear terms are studied. A new method is provided to show that the solutions will blow up in a finite time, if the nonlinear powers satisfy some conditions. The method is based on constructing appropriate test functions, by using the solution of an ordinary differential equation. It may be useful to prove the nonexistence for global solutions for other nonlinear evolution equations.
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页数：10
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