Solvability of certain one-dimensional semilinear hyperbolic systems and hyperbolic Liouville equation

Abstract

We study the initial-value problem for semilinear hyperbolic systems in one space dimension. When the power of nonlinearity is even $(n=2k)$, we have global existence of solution which is related with the repulsive Liouville equation. When n = 2k−1, we may have a finite time blow-up solution which is related with the attractive Liouville equation.

Keywords:

• Semilinear hyperbolic system
• conservation law
• blow-up
• Liouville equation

2020 Mathematics Subject Classifications:

• 35L45
• 35F25
• 35L15

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (2020R1F1A1A01072197).