论文标题
Einstein-De保姆时空中半连接阻尼波方程的爆炸结果
Blow-up results for semilinear damped wave equations in Einstein-de Sitter spacetime
论文作者
论文摘要
通过使用迭代参数，我们证明了在Einstein-De保姆时空中的半连接阻尼波方程的一些爆炸结果，具有抑制项和功率非线性的时间依赖系数。然后，由于主要爆炸结果，我们猜想了关键指数的表达式，这与许多考虑模型的许多特殊情况一致，并提供了Strauss指数的自然概括。在关键案例中，我们考虑了二阶线性颂歌的非自治和参数依赖性的cauchy问题，其明确的解决方案是通过特殊函数理论来确定的。
We prove by using an iteration argument some blow-up results for a semilinear damped wave equation in generalized Einstein-de Sitter spacetime with a time-dependent coefficient for the damping term and power nonlinearity. Then, we conjecture an expression for the critical exponent due to the main blow-up results, which is consistent with many special cases of the considered model and provides a natural generalization of Strauss exponent. In the critical case, we consider a non-autonomous and parameter-dependent Cauchy problem for a linear ODE of second-order, whose explicit solutions are determined by means of special functions' theory.
