Recent Advances in Regularity of Second-order Hyperbolic Mixed Problems, and Applications

  title={Recent Advances in Regularity of Second-order Hyperbolic Mixed Problems, and Applications},
  author={Irena Lasiecka and Roberto Triggiani},
The present paper centers on second-order hyperbolic equations in the unknownw(t,x): $${w_{tt}} + A(x,\partial )w = f{\text{ in }}\Omega =(0,T]x\Omega $$ (1.1) augmented by initial conditions $$w(0, \cdot ) = {w_0};{\text{ }}{w_t}(0, \cdot ) = {w_1}{\text{ in }}\Omega $$ (1.2) and suitable boundary conditions either of Dirichlet type $$w{|_\Sigma } = u{\text{ in }}\Sigma = (0,T]x\Gamma ,$$ (1.3D) or else of Neumann type $$\frac{{\partial w}}{{\partial {\nu _A… 

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