Analysis of nonlinear poroviscoelastic flows with discontinuous porosities

Markus Bachmayr; Simon Boisserée; Lisa Maria Kreusser

doi:10.1088/1361-6544/ad0871

Analysis of nonlinear poroviscoelastic flows with discontinuous porosities

Markus Bachmayr, Simon Boisserée, Lisa Maria Kreusser

RWTH Aachen University

Research output: Contribution to journal › Article › peer-review

Abstract

Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear interaction between porosity and effective pressure, which in certain cases leads to porosity waves. In particular, conditions for well-posedness in the presence of initial porosities with jump discontinuities are identified.

Original language	English
Pages (from-to)	7025-7064
Number of pages	40
Journal	Nonlinearity
Volume	36
Issue number	12
Early online date	13 Nov 2023
DOIs	https://doi.org/10.1088/1361-6544/ad0871
Publication status	Published - 1 Dec 2023

Bibliographical note

Funding Information:
M B acknowledges funding by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project Numbers 233630050, 442047500 – TRR 146, SFB 1481. S B has been funded in part by the M3ODEL consortium at Johannes Gutenberg University Mainz: L M K acknowledges support from Magdalene College, Cambridge (Nevile Research Fellowship).

Funding Information:
The authors would like to thank Evangelos Moulas for introducing them to the models discussed in this work and for helpful discussions.

Publisher Copyright:
© 2023 IOP Publishing Ltd & London Mathematical Society

Keywords

28A80
existence and uniqueness of solutions
magma equations
nonlinear systems of partial differential equations
nonsmooth data
poroviscoelastic flow

ASJC Scopus subject areas

General Physics and Astronomy
Applied Mathematics
Statistical and Nonlinear Physics
Mathematical Physics

Access to Document

10.1088/1361-6544/ad0871

https://arxiv.org/abs/2302.12166

Cite this

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title = "Analysis of nonlinear poroviscoelastic flows with discontinuous porosities",

abstract = "Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear interaction between porosity and effective pressure, which in certain cases leads to porosity waves. In particular, conditions for well-posedness in the presence of initial porosities with jump discontinuities are identified.",

keywords = "28A80, existence and uniqueness of solutions, magma equations, nonlinear systems of partial differential equations, nonsmooth data, poroviscoelastic flow",

author = "Markus Bachmayr and Simon Boisser{\'e}e and Kreusser, {Lisa Maria}",

note = "Funding Information: M B acknowledges funding by Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project Numbers 233630050, 442047500 – TRR 146, SFB 1481. S B has been funded in part by the M3ODEL consortium at Johannes Gutenberg University Mainz: L M K acknowledges support from Magdalene College, Cambridge (Nevile Research Fellowship). Funding Information: The authors would like to thank Evangelos Moulas for introducing them to the models discussed in this work and for helpful discussions. Publisher Copyright: {\textcopyright} 2023 IOP Publishing Ltd & London Mathematical Society",

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AU - Boisserée, Simon

AU - Kreusser, Lisa Maria

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N2 - Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear interaction between porosity and effective pressure, which in certain cases leads to porosity waves. In particular, conditions for well-posedness in the presence of initial porosities with jump discontinuities are identified.

AB - Existence and uniqueness of solutions is shown for a class of viscoelastic flows in porous media with particular attention to problems with nonsmooth porosities. The considered models are formulated in terms of the time-dependent nonlinear interaction between porosity and effective pressure, which in certain cases leads to porosity waves. In particular, conditions for well-posedness in the presence of initial porosities with jump discontinuities are identified.

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KW - existence and uniqueness of solutions

KW - magma equations

KW - nonlinear systems of partial differential equations

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Analysis of nonlinear poroviscoelastic flows with discontinuous porosities

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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