Differential and Integral Equations

Global existence of solutions for a system of nonlinear damped wave equations

Takayoshi Ogawa and Hiroshi Takeda

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We consider the Cauchy problem of the semilinear damped wave system: \begin{equation} \notag \begin{cases} \partial_{t}^2 u_{j} - \Delta u_{j} + \partial_{t} u_{j} = F_{j}(u), & t > 0, \quad x\in \mathbb R^{n},\\ u_{j}(0,x)=a_{j}(x),\quad \partial_{t} u_{j}(0,x) = b_{j}(x), & x\in \mathbb R^{n}, \end{cases} \end{equation} where $m \ge 2$ and $j = 1$, $\cdots$, $m$. We show the existence of a global-in-time solution for a small initial data under a sharp condition on the nonlinear exponents, which is a natural extension of the results for the single nonlinear damped wave equations ([28], [30]). The proof is based on $L^{p}$-$L^{q}$ type estimates of the fundamental solutions of the linear damped wave equations ([9]) and systematic choice of the function scale to adjust the nonlinear growth order.

Article information

Differential Integral Equations, Volume 23, Number 7/8 (2010), 635-657.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35L70: Nonlinear second-order hyperbolic equations 35L15: Initial value problems for second-order hyperbolic equations


Ogawa, Takayoshi; Takeda, Hiroshi. Global existence of solutions for a system of nonlinear damped wave equations. Differential Integral Equations 23 (2010), no. 7/8, 635--657. https://projecteuclid.org/euclid.die/1356019188

Export citation