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

Graziano Guerra, Wen Shen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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].

Original languageEnglish (US)
Pages (from-to)1491-1507
Number of pages17
JournalCommunications in Mathematical Sciences
Volume19
Issue number6
DOIs
StatePublished - 2021

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

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