2025/09/08 by Luis Gustavo Longen, Longen, Luis Gustavo
Engineering · Computer Science · Mathematics · #Stability and Controllability of Differential Equations #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods
paper · pdf · doi:10.48550/arxiv.2509.06671
In this paper, we study a mixed wave-plate equation with rotational inertia, fractional damping and memory non-linearity. This research is a non-existence counterpart to a paper by D'Abbicco and Longen, in search of the critical exponent for the global in-time existence of small data solutions to the Cauchy problem for a mixed wave-plate equation, with a rotational inertia and a non-integer dissipation term and a memory-type non-linearity. We employ a modified test function argument to show that there are arbitrarily small initial data for which there are no solutions for the problem in the subcritical case. Additionally, we show non-existence of global solutions in the critical case when the memory exponent is greater than (n-2)/n.