Blowup for nonlinearly damped viscoelastic equations with logarithmic source and delay terms

Advances in Difference Equations

Sun-Hye Park¹ 

[1] Office for Education Accreditation, Pusan National University, Busan, South Korea;

关键词: Blowup;    Viscoelastic equation;    Logarithmic source;    Time delay;    Nonlinear dissipation;    35L05;    35L70;    35B44;   

DOI  :  10.1186/s13662-021-03469-8

来源: Springer

【 摘 要 】

In this work, we investigate blowup phenomena for nonlinearly damped viscoelastic equations with logarithmic source effect and time delay in the velocity. Owing to the nonlinear damping term instead of strong or linear dissipation, we cannot apply the concavity method introduced by Levine. Thus, utilizing the energy method, we show that the solutions with not only non-positive initial energy but also some positive initial energy blow up at a finite point in time.

【 授权许可】

CC BY