Tariel Kiguradze

Global and Blow-Up Solutions of a Characteristic Initial Value Problem for Second Order Nonlinear Hyperbolic Equations

abstract:
It is proved that the characteristic initial value problem for the second order hyperbolic equation
\begin{equation*} u_{xy} = f(x,y,u), \end{equation*}
where $f: [0,a] \times [0,b] \times \mathbb{R} \to \mathbb{R}$ is a continuous function, has at least one global, or local blow-up solution. Unimprovable in a sense conditions of existence and nonexistence of global and local blow-up solutions are established.

Mathematics Subject Classification: 35L15, 35L70

Key words and phrases: Nonlinear hyperbolic equation, characteristic initial value problem, global solution, local blow-up solution