Bifurcating solutions to the monodomain model equipped with FitzHugh-Nagumo kinetics.
Bifurcations in a modulation equation for alternans in a cardiac fiber
While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wave-like spatial dependence, either stationary or travelling, which is known as discordant alternans. We study these phenomena in simple cardiac models through a modulation equation proposed by Echebarria-Karma. As shown in our previous paper, the zero solution of their equation may lose...
Blow-up analysis for a semilinear parabolic equation with nonlinear memory and nonlocal nonlinear boundary condition.
Blowup analysis for a semilinear parabolic system with nonlocal boundary condition.
Blowup properties for a semilinear reaction-diffusion system with nonlinear nonlocal boundary conditions.
Blow-up results for some reaction-diffusion equations with time delay
We discuss the effect of time delay on blow-up of solutions to initial-boundary value problems for nonlinear reaction-diffusion equations. Firstly, two examples are given, which indicate that the delay can both induce and prevent the blow-up of solutions. Then we show that adding a new term with delay may not change the blow-up character of solutions.