Travelling wave solutions for degenerate pseudo-parabolic equation modelling two-phase flow in porous media

C.J. Duijn, van, Y. Fan, L.A. Peletier, I.S. Pop

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Abstract

We discuss a pseudo-parabolic equation modelling two-phase flow in porous media, which includes dynamic effects in the capillary pressure. We extend the results obtained previously for linear higher order terms and investigate the existence of travelling wave solutions in the non-linear and degenerate case. This case leads to non-smooth travelling waves, as well as to a discontinuous capillary pressure. Keywords: Dynamic capillary pressure; Non-linear; Degenerate; Pseudo-parabolic equations; Sharp travelling waves
Original languageEnglish
Pages (from-to)1361-1383
JournalNonlinear Analysis : Real World Applications
Volume14
Issue number3
DOIs
Publication statusPublished - 2013

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Pseudoparabolic Equations
Degenerate Equations
Flow in Porous Media
Capillarity
Two-phase Flow
Traveling Wave Solutions
Two phase flow
Porous materials
Traveling Wave
Modeling
Linear Order
Higher Order
Term
Traveling wave solutions
Porous media
Traveling wave

Cite this

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title = "Travelling wave solutions for degenerate pseudo-parabolic equation modelling two-phase flow in porous media",
abstract = "We discuss a pseudo-parabolic equation modelling two-phase flow in porous media, which includes dynamic effects in the capillary pressure. We extend the results obtained previously for linear higher order terms and investigate the existence of travelling wave solutions in the non-linear and degenerate case. This case leads to non-smooth travelling waves, as well as to a discontinuous capillary pressure. Keywords: Dynamic capillary pressure; Non-linear; Degenerate; Pseudo-parabolic equations; Sharp travelling waves",
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Travelling wave solutions for degenerate pseudo-parabolic equation modelling two-phase flow in porous media. / Duijn, van, C.J.; Fan, Y.; Peletier, L.A.; Pop, I.S.

In: Nonlinear Analysis : Real World Applications, Vol. 14, No. 3, 2013, p. 1361-1383.

Research output: Contribution to journalArticleAcademicpeer-review

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T1 - Travelling wave solutions for degenerate pseudo-parabolic equation modelling two-phase flow in porous media

AU - Duijn, van, C.J.

AU - Fan, Y.

AU - Peletier, L.A.

AU - Pop, I.S.

PY - 2013

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N2 - We discuss a pseudo-parabolic equation modelling two-phase flow in porous media, which includes dynamic effects in the capillary pressure. We extend the results obtained previously for linear higher order terms and investigate the existence of travelling wave solutions in the non-linear and degenerate case. This case leads to non-smooth travelling waves, as well as to a discontinuous capillary pressure. Keywords: Dynamic capillary pressure; Non-linear; Degenerate; Pseudo-parabolic equations; Sharp travelling waves

AB - We discuss a pseudo-parabolic equation modelling two-phase flow in porous media, which includes dynamic effects in the capillary pressure. We extend the results obtained previously for linear higher order terms and investigate the existence of travelling wave solutions in the non-linear and degenerate case. This case leads to non-smooth travelling waves, as well as to a discontinuous capillary pressure. Keywords: Dynamic capillary pressure; Non-linear; Degenerate; Pseudo-parabolic equations; Sharp travelling waves

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DO - 10.1016/j.nonrwa.2012.10.002

M3 - Article

VL - 14

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EP - 1383

JO - Nonlinear Analysis : Real World Applications

JF - Nonlinear Analysis : Real World Applications

SN - 1468-1218

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ER -