The main goal of this paper is to prove [Formula: see text]-comparison and contraction principles for weak solutions PDE system corresponding a phase transition diffusion model Hele-Shaw type with addition linear drift. flow considered source term subject mixed homogeneous boundary conditions: Dirichlet Neumann. can be focused instance biological applications including multi-species diffusion-a...

A Hele-Shaw cell is a device used to study fluid flow between two parallel plates separated by small gap. The governing equation of within Darcy's law, which also describes through porous medium. In this work, we derive generalization law starting from three-dimensional with parity-broken viscosity tensor no isotropy. We discuss the observable effects parity-odd fluids in various physical setup...

A Hele–Shaw quadratic flow in the form of a six-port microfluidic device is employed to study deformation single channel-spanning or Newtonian drop suspended medium. An initially circular deforms into regular triarcle, i.e., rounded-corner triangle. Theoretically, calculated limit small capillary number, which defined as Ca=Cμa4/(4γb2), where C rate, μ suspending fluid viscosity, radius, γ inte...

Diurnal continental shelf waves (CSWs) are studied theoretically for an idealized topography. Wave attenuation is caused by the exchange of fluid on sloping with inner region through a permeable coastline. As example, we consider outside Lofoten-Vesterålen in north Norway. Here CSWs diurnal tidal frequencies possible small wave number range centered around zero group velocity. A previous invest...