Existence and decay rates for a semilinear dissipative fractional second order evolution equation

Authors

DOI:

https://doi.org/10.5902/2179460X40996

Keywords:

Plate/Boussinesq type equation, Fractional Laplacians, Generalized rotational inertia, Fractional dissipation, Existence and uniqueness, Decay rates

Abstract

In this work we study the existence and uniqueness of solutions and decay rates to the total energy and the L2-norm of solution for a semilinear second order evolution equation with fractional damping term and under effects of a generalized rotational inertia term in the case of plate equation. This system also includes equations of Boussinesq type that model hydrodynamic problems. We show decay rates depend- ing on the fractional powers of the operators and using an asymptotic expansion of the solution to the linear problem, we prove for some cases depending on the exponents of the operators, the optimality of the decay rates.

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Author Biographies

Ruy Coimbra Charão, Universidade Federal de Santa Catarina, Florianópolis, SC

 Professor Titular da Universidade Federal de Santa Catarina

Jaqueline Luiza Horbach, Universidade Federal de Santa Catarina, Florianópolis, SC

Doutora em Matemática pela Universidade Federal de Santa Catarina

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Published

2020-09-03

How to Cite

Charão, R. C., & Horbach, J. L. (2020). Existence and decay rates for a semilinear dissipative fractional second order evolution equation. Ciência E Natura, 42, e37. https://doi.org/10.5902/2179460X40996

Issue

Vol. 42 (2020): 40 years special anniversary edition

Section

40 YEARS - Anniversary Special Edition

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