Classical solutions of boundary value problems of Carleman equation (Q1175590)

Applying semigroup theory for accretive operators in \(L_ 1((0,1))\) the author shows existence of a global solution to the initial boundary value problem for the Carleman system \[ \partial_ t{U_ 1\brack U_ 2}+{1\quad 0\brack 0 -1}\partial_ x{U_ 1\brack U_ 2}+{U^ 2_ 1- U^ 2_ 2\brack U^ 2_ 2-U_ 1^ 2}=0 \] in the interval \([0,1]\), with inhomogeneous, time-dependent, non-negative boundary data in \(C_ 1([0,\infty))\) prescribed for the solution at \(x=0\) and non-negative initial data in \(C_ 1([0,1])\) satisfying a compatibility condition (steming from the Carleman equations evaluated at \(t=0\) and \(x=0,1)\). The result is obtained by showing that a mild solution is also classical under these assumptions.