Details

Giuseppe Maria Coclite ^[a] and Lorenzo di Ruvo ^[b]

The porous medium equation with capillary pressure effects

Pages: 173-190
Received: 31 March 2023
Accepted in revised form: 4 July 2023
Mathematics Subject Classification: 35G25, 35K55.
Keywords: Existence, uniqueness, stability, porous medium equation, Cauchy problem.
Authors address:
[a]: Politecnico di Bari, Dipartimento di Meccanica, Matematica e Management, Bari, Italy
[b]: Università di Bari, Dipartimento di Matematica, Bari, Italy

The authors are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). GMC has been partially supported by the Research Project of National Relevance ''Multiscale Innovative Materials and Structures'' granted by the Italian Ministry of Education, University and Research (MIUR Prin 2017, project code 2017J4EAYB and the Italian Ministry of Education, University and Research under the Programme Department of Excellence Legge 232/2016 (Grant No. CUP - D94I18000260001).

Abstract: We consider a third order equation, which includes pressure as a dissipative term, and describes the dynamics of two-phase flows in a porous media. It is a generalization of Benjamin-Bona-Mahony equation, which models long waves in a nonlinear dispersive system. We prove the well-posedness of the Cauchy problem, associated with this equation.

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