一个变分不等式的奇异摄动

SINGULAR PERTURBATION FOR A VARIATIONAL INEQUALITY

对变分不等式 :uε∈ Kψ={ v∈ H 20 (Ω ) |v≥ψ}ε∫ΩΔuεΔ(v - uε) dx +∫Ω Δuε Δ(v - uε) dx≥∫Ωf (v - uε) dx v∈ Kψ的奇异摄动问题进行了探索 .证明了解的重合集 Iε={ x∈Ω |uε(x) =ψ}在Hausdorff距离意义下收敛到ε=0时解的重合集 .

The singular perturbation of the variational inequalityu\-ε∈K\-ψ={v∈H\+2\-0(Ω)｜v≥ψ}, ε∫ΩΔu\-εΔ(v-u\-ε)dx+∫ΩΔu\-εΔ(v-u\-ε)dx≥∫Ωf(v-u\-ε)dx,v∈K\-ψs studied.\;It is proved that the coincidence sets I\-ε={x∈Ω｜u\-ε(x)=ψ} for the solutions converge to the coincidence set for ε=0 in the sence of Hausdorff distance.