Contact Problem With multivalued Normal compliance and Unilateral constraint

Abstract

"We presented a model for the quasi-static process of contact between an electro-viscoelastic body and a foundation. The contact was modeled with the normal compliance condition and the associated dry friction Coulomb law. The new characteristic of the model was the normal conformity as presented in the difference equation (3.7). The difficulty in solving this type of problem lies not only in the coupling of viscoelastic and electrical aspects, but also in the non-linearity of the boundary conditions modeling this type of physical phenomena (contact conditions), which gives us a quasi-variational inequality and type of nonlinear parabolic variational equalities. The existence of the weak solution of the problem was established using arguments from the theory of evolutionary variational inequalities, parabolic inequalities, and convergences of solutions. ""في مذكرتنا تطرقنا إلى حالة من حالات التلامس اللزج لجسم صلب مع سطح أملس . في البداية تطرقنا إلى بعض خواص الدوال التحليلية من ضمنها الدوال اللبشتيزية و بعض نظريات المعادلات التفاضلية المتراجحات في فضاءات مختلفة و من ثم طرح المسألة التغيرية المراد دراستها و تكون عادة صعبة فبحثنا عن مسألة مساعدة لتسهيل البحث عن الحل و تقاربه. في الأخير أثبتنا وجود الحل البسيط و تقاربه."