PreprintCC BY 4.0arXiv
Global existence for the semilinear regular Euler-Poisson-Darboux-Tricomi equation, II
Abstract
In our previous work [25], we established the global existence of solutions to the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity |u|p in the case where the damping term dominates the mass term. In contrast, this paper studies the reverse case, namely, the existence of global solutions to the equation when the mass term dominates the damping term. We prove that small-data solutions exist globally if p>max{p0((m+1)n,μ), p̃1(n,m,μ)} for δdoteq(μ−1)2−4ν2≤0, where δ measures the relative dominance between the damping and mass terms, p0(n,μ) is the \textit{Strauss-related} exponent defined by (1.12), and p̃1(n,m,μ) is defined by (2.5).
Related
- Global small data radial symmetric solutions of 3D semilinear Euler-Poisson-Darboux equations
- Existence of a separating norm for the semilinear heat equation
- Existence of infinitely many singular self-similar solutions for the semilinear heat equation
- Stochastic Euler–Poisson–Darboux Equations and a Sharp Dalang Criterion
- Poisson problem with Hardy operator on lattice graph $ \mathbb{Z}^d$ and the application to semilinear equations
BibTeX
@misc{li2026global,
title = {{Global existence for the semilinear regular Euler-Poisson-Darboux-Tricomi equation, II}},
author = {Yuequn Li and Fei Guo},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29623},
eprint = {2610.29623},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29623},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Global existence for the semilinear regular Euler-Poisson-Darboux-Tricomi equation, II
AU - Yuequn Li
AU - Fei Guo
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29623
UR - https://arxiv.org/abs/2610.29623
AB - In our previous work [25], we established the global existence of solutions to the semilinear Euler-Poisson-Darboux-Tricomi equation with power nonlinearity |u|^p in the case where the damping term dominates the mass term. In contrast, this paper studies the reverse case, namely, the existence of global solutions to the equation when the mass term dominates the damping term. We prove that small-data solutions exist globally if p>max{p_0((m+1)n,μ), p̃_1(n,m,μ)} for δdoteq(μ−1)^2−4ν^2≤0, where δ measures the relative dominance between the damping and mass terms, p_0(n,μ) is the \textit{Strauss-related} exponent defined by (1.12), and p̃_1(n,m,μ) is defined by (2.5).
ER -