发表机构
Instituto de Matemática e Estatística, Universidade Federal do Rio Grande do Sul（南里奥格兰德联邦大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明具有递减传播速度和振荡质量项的半线性移位Tricomi方程在临界Strauss型指数下发生有限时间爆破，并给出小初值情形下寿命的临界指数上界。
AI 中文摘要
我们研究了具有递减传播速度和振荡尺度不变质量的半线性移位Tricomi方程的有限时间爆破。我们聚焦于Strauss型临界区域，并证明：对于满足适当局部化条件的非负非平凡能量数据所引发的具有有限传播速度的每一个弱解，都会在有限时间内爆破。对于足够小的初始数据，我们还获得了相应的临界指数上界寿命估计。证明依赖于齐次伴随方程的一个正自相似解，该解由高斯超几何函数表示。结合先前建立的非线性项下界和适用于临界情形的新估计，这一构造将偏微分方程问题归结为一个非线性微分不等式。随后，一个常微分方程比较论证同时给出了有限时间爆破和寿命估计。
英文摘要
We study finite-time blow-up for a semilinear shifted Tricomi equation with decreasing propagation speed and an oscillatory scale-invariant mass. We focus on the Strauss-type critical regime and prove that every weak solution with finite speed of propagation, arising from nonnegative nontrivial energy data satisfying a suitable localization condition, blows up in finite time. For sufficiently small initial data, we also obtain the corresponding critical exponential upper bound for the lifespan. The proof relies on a positive self-similar solution of the homogeneous adjoint equation represented by the Gauss hypergeometric function. Combined with a previously established lower bound for the nonlinear term and new estimates adapted to the critical case, this construction reduces the PDE problem to a nonlinear differential inequality. An ODE comparison argument then yields both finite-time blow-up and the lifespan estimate.
