Structural stability and data dependence for fully nonlinear hyperbolic mixed problems
Using the results of [the author, Commun. Pure Appl. Math. 46, No. 2, 221-259 (1993; Zbl 0791.35102)] the author proves continuous dependence of the solutions of nonlinear second order hyperbolic initial boundary value problems \[ \partial^ 2_ t u- \partial_ i(a_ i(\nabla u))= f\quad\text{in }\Omega\times [0,T], \] \[ a_ i(\nabla u)\nu_ i+ b(u)=g\quad\text{in }\partial\Omega\times [0,T],\;u(0)= u_ 0,\;\partial_ t u(0)= u_ 1, \] where \(\Omega\subset\mathbb{R}^ n\) is a bounded domain with smooth boundary and unit outward normal \((\nu_ 1,\dots,\nu_ n)\) to \(\partial\Omega\), on the data \(a_ i\), \(b\), \(f\), \(g\), \(u_ 0\) and \(u_ 1\).
nonlinear second order hyperbolic initial boundary value problems
scientific article; zbMATH DE number 78048