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

@inproceedings{Lasiecka1994RecentAI,
title={Recent Advances in Regularity of Second-order Hyperbolic Mixed Problems, and Applications},
author={Irena Lasiecka and Roberto Triggiani},
year={1994}
}
• Published 1994
• Mathematics
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 $$\frac{{\partial w}}{{\partial {\nu _A… 48 Citations • Mathematics • 2013 We consider a second-order hyperbolic equation defined on an open bounded domain \Omega in \mathbb{R}^n for n \geq 2, with C^2-boundary \Gamma = \partial \Omega = \overline{\Gamma_0 \cup • Mathematics • 2008 We consider the problem of uniform stabilization of nonlinear hyperbolic equations, epitomized by the following three canonical dynamics: (1) the wave equation in the natural state space L2() × H −1 • Mathematics • 1998 We show herein the uniform stability of a thermoelastic plate model with no added dissipative mechanism on the boundary (uniform stability of a thermoelastic plate with added boundary dissipation was • Mathematics • 1999 In this work, we derive stability properties for a nonlinear thermoelastic plate system in which the higher order “free” boundary conditions are enforced on the displacement of the plate. The class • Mathematics • 1998 The paper deals with an approach to the Inverse Problems based upon their relations to the Boundary Control Theory (the BC-method). A possibility to recover a velocity c = ("") ?1=2 via response • Mathematics • 1999 Abstract The aim of this paper is to give a full analysis of the the shape differentiability for the solution to the second order hyperbolic equation with Dirichlet boundary conditions. The implicit ## References SHOWING 1-10 OF 57 REFERENCES • Mathematics • 1972 7 Scalar and Vector Ultra-Distributions.- 1. Scalar-Valued Functions of Class Mk.- 1.1 The Sequences {Mk}.- 1.2 The Space$${D_{{M_k}}}\left( H \right)$$.- 1.3 The Spaces$${D_{{M_k}}}\left( H
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