Existence, uniqueness and analyticity of solutions to boundary value problems for equations of mixed type in a half space (Q1092239)

The author considers the boundary value problem \[ u_{xx}+q(x)u_{tt}=0,\quad (x,t)\in (0,\infty)\times {\mathbb{R}};\quad \lim_{x\to 0} u(x,t)=g(t),\quad \lim_{x\to \infty} u(x,t)=0,\quad t\in {\mathbb{R}}, \] where q(x) is a real valued bounded smooth function and \(\overline{\lim}_{x\to \infty} q(x)<0\). Using the Fourier-Laplace transform with respect to t he obtains existence and uniqueness theorems, estimates for the solution and proves the analyticity in t of u(x,t) for fixed x larger than inf\(\{\) \(x: q(x)>0\}\).