On a nonlinear time-fractional cable equation

Abstract

<p>A nonlinear time-fractional cable equation posed on the interval $ (0, 1) $ under a homogeneous Dirichlet boundary condition is investigated in this work. The considered equation reflects the anomalous electro-diffusion in nerve cells. Using nonlinear capacity estimates specifically adapted to the considered problem, we establish sufficient conditions for the nonexistence of weak solutions.</p>