TY - JOUR
T1 - The Cauchy Problem For A Non Strictly Hyperbolic 3×3 System Of Conservation Laws Arising In Polymer Flooding
AU - Guerra, Graziano
AU - Shen, Wen
N1 - Funding Information:
Acknowledgment. The present work was supported by the PRIN 2015 project Hyperbolic Systems of Conservation Laws and Fluid Dynamics: Analysis and Applications and by GNAMPA 2019 project Equazioni alle derivate parziali di tipo iperbolico o non locale ed applicazioni. The authors would like to thank the anonymous referee for carefully reading the manuscript and providing many useful suggestions.
Publisher Copyright:
© 2021 International Press
PY - 2021
Y1 - 2021
N2 - 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
AB - 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
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U2 - 10.4310/CMS.2021.v19.n6.a2
DO - 10.4310/CMS.2021.v19.n6.a2
M3 - Article
AN - SCOPUS:85120939682
SN - 1539-6746
VL - 19
SP - 1491
EP - 1507
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 6
ER -