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arXiv · 2308.01272

Blow-up and lifespan estimate for the generalized tricomi equation with the scale-invariant damping and time derivative nonlinearity on exterior domain

Makram Hamouda·Mohamed Ali Hamza·Bouthaina Yousfi
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Abstract

The article is devoted to investigating the initial boundary value problem for the damped wave equation in the scale-invariant case with time-dependent speed of propagation on the exterior domain. By presenting suitable multipliers and applying the test-function technique, we study the blow-up and the lifespan of the solutions to the problem with derivative-type nonlinearity $ \d u_{tt}-t^{2m}\Delta u+\frac{\mu}{t}u_t=|u_t|^p, \quad \mbox{in}\ \Omega^{c}\times[1,\infty),$ that we associate with appropriate small initial data.

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Makram Hamouda, Mohamed Ali Hamza, Bouthaina Yousfi. 2023-08-02. Blow-up and lifespan estimate for the generalized tricomi equation with the scale-invariant damping and time derivative nonlinearity on exterior domain. https://arxiv.org/abs/2308.01272

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