In this work, we prove the existence of global (in time) small data solutions for wave equations with two dissipative terms and with power nonlinearity \(|u|^p\) or nonlinearity of derivative type \(|u_t|^p\), in any space dimension \(n\geqslant 1\), for supercritical powers \(p>{\bar{p}}\). The presence of two dissipative terms strongly influences the nature of the problem, allowing us to derive \(L^r-L^q\) long time decay estimates for the solution in the full range \(1\leqslant r\leqslant q\leqslant \infty \). The optimality of the critical exponents is guaranteed by a nonexistence result for subcritical powers \(p<{\bar{p}}\).

在这项工作中，我们证明了具有两个耗散项和功率非线性\(|u|^p\)或导数类型\(|u_t|^p\ ) 的波动方程的全局（在时间上）小数据解的存在性)，在任何空间维度 \(n\geqslant 1\)，对于超临界功率 \(p>{\bar{p}}\)。两个耗散项的存在强烈影响问题的性质，使我们能够推导出\(L^rL^q\)全范围内解的长时间衰减估计\(1\leqslant r\leqslant q\leqslant \ infty \)。临界指数的最优性由次临界幂\(p<{\bar{p}}\)的不存在结果保证 。