Inclusion of solutions of Darboux problems for quasilinear hyperbolic equations

摘要

We deal with the characteristic initial value problem for a hyperbolic differential equationa(x,y,u)uxx+b(x,y,u)uxy+c(x,y,u)uyy=f(x,y,u,ux,uy).The paper presents a method which yields pointwise enclosures of the domain of determinacy M̂ (depending implicitly on u) and of the corresponding solution u(x,y),(x,y)∈M̂. The method has been implemented on a computer using machine interval arithmetic.