On the global solution problem for semilinear generalized Tricomi equations, I

2015/11/27 by He, Daoyin, Witt, Ingo, Yin, Huicheng · 2 citations
#35L65 #35L67 #35L70 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1511.08722

Abstract

In this paper, we are concerned with the global Cauchy problem for the semilinear generalized Tricomi equation ∂_t² u-t^m Δu=|u|^p with initial data (u(0,⋅), ∂_t u(0,⋅))= (u₀, u₁), where t≥ 0, x∈\mathbb Rⁿ (n≥ 3), m∈\mathbb N, p>1, and u_i∈ C₀^∞(\mathbb Rⁿ) (i=0,1). We show that there exists a critical exponent p_crit(m,n)>1 such that the solution u, in general, blows up in finite time when 1 p_crit(m,n) such that the solution u exists globally when p>p_conf(m,n) provided that the initial data is small enough. In case p_crit(m,n)

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