Periodic waves in unsaturated porous media with hysteresis
Bettina DetmannUniversität Duisburg-Essen, Germany
Pavel KrejčíAcademy of Sciences, Prague, Czechia
Elisabetta RoccaUniversità degli Studi di Pavia, Italy
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We consider a PDE system with degenerate hysteresis describing unsaturated flow in 3D porous media. Assuming that a time periodic forcing is prescribed on the boundary, we prove that a time periodic response exists as long as the amplitude of the forcing terms is small enough to keep the solution within the convexity domain of the hysteresis operator.