Existence, uniqueness, and stability for a class of diffusion problems

摘要

Singular boundary value problems are used to model diffusion of a specimen in a nonhomogeneous environment. Existence and uniqueness results are obtained by establishing a priori bounds for all solutions and then applying a shooting technique to appropriate initial value problems. Asymptotic stability results are obtained by constructing an appropriate Lyapunov function and deriving differential inequalities to be satisfied by the parameters of the problem.