Global solutions for a semilinear, two-dimensional Klein-Gordon equation with exponential-type nonlinearity

Global existence, blow up and asymptotic

Global existence, blow up and asymptotic behaviour of solutions for nonlinear Klein–Gordon equation with dissipative term

✍ Xu Runzhang 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 203 KB

## Abstract We study the Cauchy problem of nonlinear Klein–Gordon equation with dissipative term. By introducing a family of potential wells, we derive the invariant sets and prove the global existence, finite time blow up as well as the asymptotic behaviour of solutions. In particular, we show a s