This paper addresses a nonlinear partial differential control system arising in population
dynamics. The system consist of three diffusion equations describing the evolutions of three …

We consider a scalar conservation law with hysteresis in which the flux function depends on
the history of the evolution. The work is motivated by the need to account for hysteresis in …

This paper is concerned with a population dynamics model describing the evolution of three
biological species. Our system takes into account diffusion and hysteretic effects underlying …

A PDE system consisting of the mechanical equilibrium and mass balance equations for
displacement and capillary pressure as a model for fluid diffusion in a partially saturated …

In this paper, a continuum model is introduced for fluid flow in a deformable porous medium,
where the fluid may undergo phase transitions. Typically, such problems arise in modeling …

The full quasistatic thermomechanical system of PDEs, describing water diffusion with the
possibility of freezing and melting in a visco-elasto-plastic porous solid, is studied in detail …

A nonlinear partial differential control system is considered. This system arises, for instance,
when modeling the evolution of populations in the vegetation–prey–predator framework. Our …

We propose a model for multicomponent flow of immiscible fluids in a deformable porous
medium accounting for capillary hysteresis. Oil, water, and air in the soil pores offer a typical …

The diffusion equation with a bounded saturation range under the time derivative and with
Robin boundary conditions is shown to admit a regular bounded solution provided that the …

This paper addresses a nonlinear partial differential control system arising in population
dynamics. The system consist of three diffusion equations describing the evolutions of three …