On the existence of low regularity solutions to semilinear generalized Tricomi equations in mixed type domains

2014/09/02 by Zhuoping Ruan, Ruan, Zhuoping, Ingo Witt +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1409.0707

openalex publication_date 2014/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In [19-20], we have established the existence and singularity structures of low regularity solutions to the semilinear generalized Tricomi equations in the degenerate hyperbolic regions and to the higher order degenerate hyperbolic equations, respectively. In the present paper, we shall be concerned with the low regularity solution problem for the semilinear mixed type equation \p_t²u-t^2l-1Δu= f(t,x,u) with an initial data u(0,x)=φ(x)∈ H^s(\Bbb Rⁿ) (0≤ s0.

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