Initial boundary value problems for the Carleman equation
The author utilizes the theory of nonlinear evolution operators to investigate the coupled first order hyperbolic system \[ \partial u/\partial t+\partial u/\partial x+u^ 2-v^ 2=0\quad u(0,t)=g(t),\quad v(1,t)=h(t) \] \[ \partial v/\partial t-\partial v/\partial x+v^ 2-u^ 2=0\quad u(x,0)=u_ 0(x),\quad v(x,0)=v_ 0(x) \] He associates a nonlinear evolution system in \(L^ 1(0,1)\) with (1); this system is generated by a family of nonlinear accretive operators of varying domain. In case that the boundary conditions are constant, the system is autonomous. Consequently the evolution operator is a nonlinear semigroup.
scientific article; zbMATH DE number 3865839
scientific article