Cauchy problem for weakly linearly degenerate hyperbolic systems in diagonal form Original Research Article

We study the Cauchy problem for quasi-linear strictly hyperbolic systems of diagonal form with weakly linearly degenerate characteristics. The global existence and uniqueness of C1 solution with initial data ϕ in View the MathML source are proved when the View the MathML source norm of ϕ or the View the MathML source norm of ϕ′ is small. We also give some examples to show that if the initial data are not in View the MathML source or not small, then the solution to the Cauchy problem may blow up in a finite time.