We Study The Cauchy Problem Of A 3×3 System Of Conservation Laws Modeling Two–Phase Flow Of Polymer Flooding In Rough Porous Media With Possibly Discontinuous Permeability Function. The System Loses Strict Hyperbolicity In Some Regions Of The Domain Where The Eigenvalues Of Different Families Coincide, And Bv Estimates Are Not Available In General. For A Suitable 2×2 System, A Singular Change Of Variable Introduced By Temple [B. Temple, Adv. Appl. Math., 3(3):335–375, 1982], [E.L.Isaacson And J.B. Temple, J. Diff. Eqs., 65(2):250–268, 1986] Could Be Effective To Control The Total Variation [W. Shen, J. Diff. Eqs., 261(1):627–653, 2016]. An Extension Of This Technique Can Be Applied To A 3×3 System Only Under Strict Hypotheses On The Flux Functions [G.M. Coclite And N.H. Risebro, Siam J. Math. Anal., 36(4):1293–1309, 2005]. In This Paper, Through An Adapted Front Tracking Algorithm We Prove The Existence Of Solutions For The Cauchy Problem Under Mild Assumptions On The Flux Function, Using A Compensated Compactness Argument

Guerra, G., Shen, W. (2021). The Cauchy Problem For A Non Strictly Hyperbolic 3×3 System Of Conservation Laws Arising In Polymer Flooding. COMMUNICATIONS IN MATHEMATICAL SCIENCES, 19(6), 1491-1507 [10.4310/CMS.2021.v19.n6.a2].

The Cauchy Problem For A Non Strictly Hyperbolic 3×3 System Of Conservation Laws Arising In Polymer Flooding

Guerra G.;
2021

Abstract

We Study The Cauchy Problem Of A 3×3 System Of Conservation Laws Modeling Two–Phase Flow Of Polymer Flooding In Rough Porous Media With Possibly Discontinuous Permeability Function. The System Loses Strict Hyperbolicity In Some Regions Of The Domain Where The Eigenvalues Of Different Families Coincide, And Bv Estimates Are Not Available In General. For A Suitable 2×2 System, A Singular Change Of Variable Introduced By Temple [B. Temple, Adv. Appl. Math., 3(3):335–375, 1982], [E.L.Isaacson And J.B. Temple, J. Diff. Eqs., 65(2):250–268, 1986] Could Be Effective To Control The Total Variation [W. Shen, J. Diff. Eqs., 261(1):627–653, 2016]. An Extension Of This Technique Can Be Applied To A 3×3 System Only Under Strict Hypotheses On The Flux Functions [G.M. Coclite And N.H. Risebro, Siam J. Math. Anal., 36(4):1293–1309, 2005]. In This Paper, Through An Adapted Front Tracking Algorithm We Prove The Existence Of Solutions For The Cauchy Problem Under Mild Assumptions On The Flux Function, Using A Compensated Compactness Argument
Articolo in rivista - Articolo scientifico
Compensated Compactness; Conservation Laws; Degenerate Systems; Discontinuous Flux; Polymer Flood-ing; Wave Front Tracking;
English
2-ago-2021
2021
19
6
1491
1507
partially_open
Guerra, G., Shen, W. (2021). The Cauchy Problem For A Non Strictly Hyperbolic 3×3 System Of Conservation Laws Arising In Polymer Flooding. COMMUNICATIONS IN MATHEMATICAL SCIENCES, 19(6), 1491-1507 [10.4310/CMS.2021.v19.n6.a2].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/342435
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