We consider quasi-stationary (travelling wave type) solutions to a nonlinear reaction-diffusion equation with arbitrary, autonomous coefficients, describing the evolution of glioblastomas, aggressive primary brain tumors that are characterized by extensive infiltration into the brain and are highly resistant to treatment. The second order nonlinear equation describing the glioblastoma growth th...

The propagating chemical fronts found in cubic autocatalytic reactiondiffusion processes are studied. Simulations of the reaction-diffusion equation near to and far from the onset of the front instability are performed and the structure and dynamics of chemical fronts are studied. Qualitatively different front dynamics are observed in these two regimes. Close to onset the front dynamics can be ...

Based on the recently introduced fractional Taylor’s formula, a fractional heat conduction constitutive equation is formulated by expanding the single-phase lag model using the fractional Taylor’s formula. Combining with the energy balance equation, the derived fractional heat conduction equation has been shown to be capable of modeling diffusion-to-Thermal wave behavior of heat propagation by ...

This paper describes a partial differential equation for denoising images. The proposed method is demonstrably superior to anisotropic diffusion (and it’s many variations) for denoising images that are approximately piecewise constant. The method relies on an equation that is the level-set equivalent of the anisotropic diffusion equation proposed by Perona and Malik [1]. This proposed equation ...

In this study the laws of mechanics for multi-component systems are used to develop a theory for the diffusion of ions in the presence of an electrostatic field. The analysis begins with the governing equation for the species velocity and it leads to the governing equation for the species diffusion velocity. Simplification of this latter result provides a momentum equation containing three domi...