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