Boundedness of global solutions for a nonlinear degenerate parabolic (porous medium) system with localized sources

Global Existence and Blow-Up for a Class of Degenerate Parabolic Systems with Localized Source

“…This system can be used to describe the development of two groups in the dynamics of biological groups where u and v are their densities. It also arises in the study of the flow of a fluid through a homogeneous isotropic rigid porous medium with internal localized source, see [3,[6][7][8]. The studies on the blow-up and global existence of solutions for the equations or systems not in divergence form with local, nonlocal or localized terms can be found in [2,4,5,[9][10][11][12][16][17][18][19][20][21].…”

A degenerate parabolic system with localized sources and nonlocal boundary condition

“…For other related work with localized sources, we refer the reader to [8][9][10][11]23,28,29,49] and the references therein.…”

Local existence and uniqueness of solutions of a degenerate parabolic system

“…In recent years, degenerate parabolic systems are of particular interests since they can take into account nonlinear diffusion occurring in the phenomena appearing in the models, and have been extensively studied by many researchers (see e.g., [3,[10][11][12][13] and the references therein). The degeneracy and coupled with nonlinear terms of this systems cause great difficulties to study them.…”