Abstract
This paper deals with initial-boundary value problems for a damped thin quasilinear plate. With restriction on the norms of the initial data, it will be established global weak and global strong solutions. It will also be shown that the strong solution is uniformly stable and unique. Furthermore, using a weak internal damping mechanism, an exponential decay estimate for the energy of weak solutions is established.
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We would like to thank the referee for the careful reading and helpful suggestions which led to a substantial improvement of our original manuscript.
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Batista, A.A., Clark, H.R., Guardia, R.R. et al. Remarks on thin quasilinear plates with mixed boundary conditions. J. Evol. Equ. 22, 54 (2022). https://doi.org/10.1007/s00028-022-00810-w
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DOI: https://doi.org/10.1007/s00028-022-00810-w
Keywords
- Quasilinear Carrier plate equations
- Quasilinear boundary conditions
- Existence
- Uniqueness
- Damping
- Energy exponential decay