First initial-boundary value problems for quasilinear hyperbolic- parabolic coupled systems (Q759912)

Under some reasonable assumptions a local in time existence and uniqueness theorem is proved for first initial-boundary value problems of general type for the following quasilinear hyperbolic-parabolic coupled system in two variables: \[ \sum^{n}_{j=1}\zeta_{\ell j}(t,x,u,v)(\partial u_ j/\partial t+\lambda_{\ell}(t,x,u,v,v_ x)\partial u_ j/\partial x)= \] \[ \zeta_{\ell}(t,x,u,v)(\partial v/\partial t+\lambda_{\ell}(t,x,u,v,v_ x)\partial v/\partial x)+\mu_{\ell}(t,x,u,v,v_ x) \] \[ (\ell =1,...,n),\quad \partial v/\partial t-a(t,x,u,v,v_ x)\partial^ 2v/\partial x^ 2=b(t,x,u,v,v_ x). \]