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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… Click to show full abstract
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.
Keywords:
damped wave;
wave equations;
nonlinear terms;
scale invariant;
invariant damped;
combined nonlinear
Journal Title: Symmetry
Year Published: 2022
Link to full text (if available)
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Journal Title: Symmetry
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!