國立清華大學 數學系

Abstract: In this talk, we study Poisson-Nernst-Planck (PNP) systems, which is one of the fundamental model the motion of charge carriers in electrolytes, semiconductors, or ion channels in cell membranes. With a small dielectric parameter $\varepsilon$ approaches to zero, PNP system admits a steady-state solution with boundary layers. For the stability of boundary layer solutions of PNP system, we estimate the solution of the perturbed problem with global electroneutrality. By transforming the perturbed problem into another parabolic system with a new and useful energy law, we prove that the $H^{-1}$-norm of the solution of the perturbed problem decays exponentially with exponent independent of $\varepsilon$. Tea Time: 3:00PM, R707