Blow-up for a semilinear Tricomi equation in the oscillatory regime at the critical Strauss-type exponent

Diego Marcon; Wanderley Nunes do Nascimento; Matheus C. Santos

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arXiv · 2609.28389

Blow-up for a semilinear Tricomi equation in the oscillatory regime at the critical Strauss-type exponent

Diego Marcon·Wanderley Nunes do Nascimento·Matheus C. Santos

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Abstract

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.

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Diego Marcon, Wanderley Nunes do Nascimento, Matheus C. Santos. 2026-09-23. Blow-up for a semilinear Tricomi equation in the oscillatory regime at the critical Strauss-type exponent. https://arxiv.org/abs/2609.28389

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