In this note, we prove a blow-up result for a semilinear generalized Tricomi equation with nonlinear term of derivative type, i.e., for the equation Tℓu=|∂tu|p, where Tℓ=∂t2-t2ℓΔ. Smooth solutions blow up in finite time for positive Cauchy data when the exponent p of the nonlinear term is below QQ-2, where Q= (ℓ+ 1) n+ 1 is the quasi-homogeneous dimension of the generalized Tricomi operator Tℓ. Furthermore, we get also an upper bound estimate for the lifespan.
A Blow-Up Result for a Generalized Tricomi Equation with Nonlinearity of Derivative Type
Lucente S.;Palmieri A.
2021-01-01
Abstract
In this note, we prove a blow-up result for a semilinear generalized Tricomi equation with nonlinear term of derivative type, i.e., for the equation Tℓu=|∂tu|p, where Tℓ=∂t2-t2ℓΔ. Smooth solutions blow up in finite time for positive Cauchy data when the exponent p of the nonlinear term is below QQ-2, where Q= (ℓ+ 1) n+ 1 is the quasi-homogeneous dimension of the generalized Tricomi operator Tℓ. Furthermore, we get also an upper bound estimate for the lifespan.File in questo prodotto:
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Lucente S., Palmieri A. (2021 MilanJM - ArXiv version) - A blow-up result for a generalized Tricomi equation with nonlinearity of derivative type.pdf
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