Justification of perturbation algorithm in a nonlinear hyperbolic problem (Q1814584)

The author proves a uniqueness theorem and an a-priori estimate for solutions \(v\in W_ 2^ 1(\Omega)\) of the problem \(-\partial v/\partial t-a(t,x)\partial v/\partial x=p(t,x)\) \(((t,x)\in\Omega=(0,T)\times(a,b);\) \(v(x,T)=0\), \(v(t,b)=0)\). The author notes that this result can be used for the verification of a perturbation algorithm for a nonlinear hyperbolic problem.