## Tsukuba Journal of Mathematics

- Tsukuba J. Math.
- Volume 35, Number 1 (2011), 13-52.

### Propagation of analyticity in the *C*^{∞}
solutions of quasi-linear weakly hyperbolic wave equations

#### Abstract

We study the propagation of the analytic regularity of the *C*^{∞}
solutions of the quasi-linear, weakly hyperbolic wave equation *u*_{
tt
} - *a*(*u*)*u*_{
xx
} = 0, where *a*(*u*) is a bounded, nonnegative analytic function.

#### Article information

**Source**

Tsukuba J. Math., Volume 35, Number 1 (2011), 13-52.

**Dates**

First available in Project Euclid: 19 July 2011

**Permanent link to this document**

https://projecteuclid.org/euclid.tkbjm/1311081447

**Digital Object Identifier**

doi:10.21099/tkbjm/1311081447

**Mathematical Reviews number (MathSciNet)**

MR2848814

**Zentralblatt MATH identifier**

1245.35073

**Subjects**

Primary: 35L70: Nonlinear second-order hyperbolic equations

Secondary: 35L80: Degenerate hyperbolic equations 35B65: Smoothness and regularity of solutions

**Keywords**

Weakly hyperbolic equations analytic regularity

#### Citation

Manfrin, R. Propagation of analyticity in the C ∞ solutions of quasi-linear weakly hyperbolic wave equations. Tsukuba J. Math. 35 (2011), no. 1, 13--52. doi:10.21099/tkbjm/1311081447. https://projecteuclid.org/euclid.tkbjm/1311081447