國立清華大學 數學系

The FitzHugh-Nagumosystem gives rise to a geometric variationalproblem when its parameters take values in a particular range as a consequence of Gamma-convergence. A stationary set of the variationalproblem satisfies an Euler-Lagrange equation that involves the curvature of its boundary, and a nonlocal term that inhibits unlimited growth and spreading. Disc shaped stationary sets in the plane, known as bubbles, are studied. A complete description of the existence and the stability of these solutions is established. Extension of similar results in higher dimension is indicated. In general such radial bubble cannot be a solution when we treat a finite domain D in the plane. We will briefly describe how to construct these droplet solutions as a perturbation of the bubbles.