分野別セミナー

(添付ファイルに数式付きの概要があります)
This talk is concerned with a strongly irreversible Allen-Cahn equation (irAC), which is a variant of the Allen-Cahn equation and describes a non-decreasing evolution of a constrained gradient flow. Such a unidirectional evolution appears in the study of Damage Mechanics, where a phase parameter is introduced to describe the degree of damage in material (hence the evolution of the phase parameter is naturally supposed to be monotone, and moreover, the evolution is often described by a sort of gradient flow). In this talk, we shall discuss asymptotic behavior of solutions to the Cauchy-Dirichlet problem for (irAC) and (Lyapunov) stability of equilibria as well as fundamental issues such as existence and uniqueness of solutions, by introducing two equivalent forms to (irAC). Particularly for stability analysis, we emphasize that equilibria are accumulating (in a proper energy space), and hence, one cannot expect asymptotic stability and we need to overcome some difficulty arising from the accumulation of equilibria. This talk is based on a joint work with Messoud Efendiev (Munchen).

添付ファイル：数式付き概要
リンク：セミナーHP
　　　　福岡大学セミナーハウスへのアクセス