Semigroup approach to the question of stability for a partial differential equation with hysteresis (Q1269604)

The author is concerned with the asymptotic behavior in the \(L^1(\Omega)\)-norm of the solutions to partial differential equations with hysteresis (PDEH). The method here is the semigroup approach in \(L^1(\Omega)\). One reduces the PDEH to a first-order differential equation associated with m-accretive operators in \(L^1(\Omega)\), whose solution can be expressed in terms of nonlinear semigroups. The results are interesting, and most of their proof is not routine.