Year: 2025
Type: preprint
Abstract: We investigate the relaxation problem for the one-dimensional pressureless Euler--Poisson equations with the initial density being a finite Radon measure. The entropy solution of this linearly degenerate hyperbolic system converges to the weak solution of part of drift--diffusion equations without diffusion term when the momentum relaxation time tends to zero. Independent of compactness, our strategy is to construct the formula of solutions to both systems and directly obtain the convergent result. Furthermore, the uniqueness of entropy solution to pressureless Euler--Poisson equations is also proved by Oleinik condition and the initially weak continuity of kinetic energy measure.
Source: arXiv (Cornell University)
Author: Tang, GuiRong
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417429526
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