| Contents |
| We study a nonlinear diffusion equation with
irreversibility condition:
$u_t=(\Delta u +f)_+$ in a bounded domain of ${\bf R}^n$
with Dirichlet or mixed boundary
condition. Under some suitable conditions, we prove
the unique existence of a strong solution and show
its gradient structure, comparison principle,
and long time 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.
An application to a phase field model of crack propagation
phenomena is also presented with some numerical examples. |
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