This work provides analytical results towards applications in the field of invasive-invaded
systems modeled with nonlinear diffusion and with advection. The results focus on showing …

In this paper, we study the properties of solutions to a degenerate parabolic equation with
variable density and absorption. We first obtain a critical exponent, which distinguishes the …

In this paper, we study the existence of local/global solutions to the Cauchy problem (ρ (x)
u< sub> t= Δu+ q (x) u< sup> p,(x, t)∈ ℝ< sup> NX (0, T), u (x, 0)= u< sub> 0(x)≤ 0, x∈ ℝ< …

We study the existence of monotone heteroclinic traveling waves for a general Fisher-
Burgers equation with nonlinear and possibly density-dependent diffusion. Such a model …

The subject of this investigation is the long time behavior of the positive solutions of the
following nonhomogeneous equation 1 ρ\left (\left| x\right|\right) ∂ β\left (v\right) ∂ tN i= 1 ∑ …

It is the objective to provide a mathematical treatment of a nonhomogeneous and non-
lipschitz reaction problem with a non-linear diffusion and advection operator, so that it can …

In this paper, we study the finite time blowup and global existence of the interfaces of the
inhomogeneous non-Newtonian polytropic filtration equation with convection ρ (x) u_t=(∣ …

The subject of this investigation is the blow-up phenomena of the positive solutions of the
mixed problem for the one-dimensional polytropic filtration equation with inhomogeneous …

This paper deals with the Cauchy problem for the equation ut=(um) xx+ b (x, t)(up) x, with m>
1, 0< p< 1, and b (x, t) being positive. First, we establish the local existence and uniqueness …