The regularity of solutions of the initial boundary value problem for quasi-linear symmetric hyperbolic systems with characteristic boundary (Q2708706)

Consider the following mixed problem: NEWLINE\[NEWLINE A_0(t,x,u)u_t+\sum_{j=1}^nA_j(t,x,u)u_{x_j}=g(t,x,u) \quad \text{in }[0,T]\times \Omega,NEWLINE\]NEWLINE NEWLINE\[NEWLINEM(x)u=0,\quad (t,x)\in [0,T]\times \partial \Omega, \qquad u(0,x)=u_0(x), \quad x\in \Omega,NEWLINE\]NEWLINE where \(\Omega\) is a bounded domain in \(\mathbb{R}^n\) with smooth boundary \(\partial \Omega\), \(A_0\) is real symmetric and positive defined matrix, \(A_j\) are real symmetric matricies. Under some algebraic conditions on matricies \(A_j\) and some regularity as well as compatibility conditions on \(u_0\), is proved the existence and regularity of the solution of the problem locally in time.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00029].