3月16日(金) 14:45 -- 15:45 木村正人 (金沢大学)
             ``Unidirectional diffusion model and application to crack 
               growth.''

＜研究発表要旨＞
We study a nonlinear diffusion equation with irreversibility condition in 
a bounded domain with the Dirichlet or a mixed boundary condition. Under 
some suitable conditions, we prove the unique existence of a strong 
solution and show its gradient structure, comparison principle, and 
longtime behaviour of the solution. The construction of the strong 
solution is done through the backward Euler time discretization by using 
a regularity estimate of the solution of the classical obstacle problem. 
As an application of our equation, we show a phase field model for crack 
propagation in elastic media and its numerical simulation. This talk is 
based on joint works with Goro Akagi (Tohoku University) and with 
Takeshi Takaishi (Hiroshima Kokusai Gakuin University).