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.
Lifespan of semilinear generalized Tricomi equation with Strauss type exponent
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abstract
In this paper, we consider the blow-up problem of semilinear generalized Tricomi equation. Two blow-up results with lifespan upper bound are obtained under subcritical and critical Strauss type exponent. In the subcritical case, the proof is based on the test function method and the iteration argument. In the critical case, an iteration procedure with the slicing method is employed. This approach has been successfully applied to the critical case of semilinear wave equation with perturbed Laplacian or the damped wave equation of scattering damping case. The present work gives its application to the generalized Tricomi equation.
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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.