## Differential and Integral Equations

### Square root of absolute value of derivative on a segment

#### Abstract

We consider the initial-boundary-value problem for a nonlinear pseudodifferential equation on a segment. We are interested in the case of a nonanalytic symbol of the pseudodifferential operator $K(p)=\sqrt{\left\vert p\right\vert }.$ We study traditionally important problems of the theory of nonlinear partial differential equations, such as global-in-time existence of solutions to the initial-boundary-value problem and the asymptotic behavior of solutions for large time.

#### Article information

Source
Differential Integral Equations, Volume 23, Number 7/8 (2010), 725-746.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356019193

Mathematical Reviews number (MathSciNet)
MR2654267

Zentralblatt MATH identifier
1240.35084

Subjects
Primary: 35Q35: PDEs in connection with fluid mechanics

#### Citation

Kaikina, Elena I.; Sánchez-Suárez, Isahi. Square root of absolute value of derivative on a segment. Differential Integral Equations 23 (2010), no. 7/8, 725--746. https://projecteuclid.org/euclid.die/1356019193