| Dedicated to Professor Constantin Fetecau on the occasion of his 80th anniversary
Alessio Famà†, Liliana Restuccia‡ Abstract: In this paper the propagation of weak discontinuity waves is investigated in a special isotropic porous medium filled by a fluid flow. To this aim we introduce a new variable related to the surface across which the first derivatives of the solutions of the governing equations undergo a jump. Following a Boillat’s methodology for quasi-linear and hyperbolic systems of the first order, we have investigated, in an one-dimensional case, the propagation of one solution into an uniform unperturbed state in the first approximation, obtaining the Bernoulli’s equation governing the evolution of the amplitude of the weak discontinuity wave, the wave front, the velocity along the characteristic rays, the approximated solution and the critical time. The results obtained can be applied in certain technical fields, such as biology, the medical sciences and geology. Keywords: weak discontinuity waves, partial differential equations, approximate solutions, non-equilibrium thermodynamics, porous media filled by a fluid flow. MSC: 35A25, 74A15, 74F10, 80A17. DOI 10.56082/annalsarscimath.2026.4.265 Read full article *Accepted for publication on October 02, 2026 |
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application,
ISSN ONLINE 2066 – 6594
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