Year: 2025
Type: preprint
Abstract: We consider an elliptic-parabolic free boundary problem that models the fluid flow through a partially saturated porous medium. The free boundary arises as the interface separating the saturated and unsaturated regions. Our main goal is to investigate, for the 1+1 dimensional model, how jump discontinuities on the boundary and initial data influence the regularity of both the solution and the free boundary. We show that if the data is merely bounded, then weak solutions are Lipschitz in space and $C^{1/2}$ in time in the unsaturated region. Moreover, the free boundary is locally the graph of a $C^{1/2}$ function, and this regularity is optimal. We view this analysis as a stepping stone towards the study of local regularization for higher-dimensional elliptic-parabolic free boundaries.
Source: arXiv (Cornell University)
Authors: Kriventsov, Dennis, Soria-Carro, María
Institution: Rutgers, The State University of New Jersey
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
OpenAlex ID: W4414536817
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