On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity

Alessandro Palmieri

On the the critical exponent for the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity

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arxiv 2105.09879 v2 pith:ZTMOTBI6 submitted 2021-05-20 math.AP

Alessandro Palmieri This is my paper · ORCID

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In this note, we derive a blow-up result for a semilinear generalized Tricomi equation with damping and mass terms having time-dependent coefficients. We consider these coefficients with critical decay rates. Due to this threshold nature of the time-dependent coefficients (both for the damping and for the mass), the multiplicative constants appearing in these lower-order terms strongly influence the value of the critical exponent, determining a competition between a Fujita-type exponent and a Strauss-type exponent.

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Lifespan estimate for the semilinear regular Euler-Poisson-Darboux-Tricomi equation
math.AP 2025-02 conditional novelty 6.0 of 10

Blow-up and a lifespan upper bound are established for the semilinear Euler-Poisson-Darboux-Tricomi equation at the Strauss critical exponent, using a new hypergeometric test function.

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