We study the blowup problems for semilinear wave equations with control function in the domain and on the boundary. Sufficient optimality conditions for controlled blowup time are derived in terms of new dynamic programming methodology. We define ε-optimal value function and we construct sufficient ε-optimal conditions for that function again in terms of new dynamic programming inequality.

中文翻译：

---

波动方程的爆破和近似最优条件的控制

我们研究了在域内和边界上具有控制功能的半线性波动方程的爆破问题。根据新的动态规划方法，得出了可控爆燃时间的充分优化条件。我们定义了ε最优值函数，并根据新的动态规划不等式再次为该函数构造了足够的ε最优条件。