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Well-Posedness of Initial-Boundary Value Problems for Piezoelectric Equations
Authors:Masayuki Akamatsu  Gen Nakamura
Institution:1. Japan Coast Guard Academy , Kure , Hiroshima , 737-8512 , Japan;2. Department of Mathematics , Hokkaido University , Sapporo, Hokkaido , 060-0810 , Japan
Abstract:The well-posedness of the initial-boundary value problems for quasi-electrostatic equations in a bounded domain with Lipschitz boundary is proved. The quasi-electrostatic equation is the coupled system of the equations of motion and the equation of the quasistatic electric field. The mass density, the elastic, piezoelectric and dielectric tensors are bounded measurable functions in the domain, and these tensors satisfy the positivity and the symmetry. The initial conditions are given only for the mechanical displacement and its time derivative. The methods of proof are Galerkin's method, duality argument and energy inequality.
Keywords:Piezoelectric Equations  Quasi-electrostatic  Well-posedness  Initial-boundary Value Problems  Mixed Boundary Conditions
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