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

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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