Cauchy problem for a nonlinear wave equation with nonlinear damping and source terms

A thermoplastic elastomer composition prepared by crosslinking a composition comprising the following components (A), (B) and (C) by using a phenolic curing agent: (A) 30-70 parts by weight of an ethylene/ alpha -olefin copolymer prepared by copolymerizing ethylene and an alpha -olefin having 3 to 12 carbon atoms in the presence of a catalyst comprising a solid component and an organoaluminum compound which solid component contains at least magnesium and titanium, said ethylene/ alpha -olefin copolymer having the following properties (I) to (IV): -(I) Melt index 0.01-100 g/10 min -(II) Density 0.860-0.910 g/cm3 -(III) Maximum peak - temperature as measured - according to a not lower than 100 DEG C. - differential scanning - calorimetry (DSC) -(IV) Insolubles in boiling - n-hexane not less than 10 wt. % - (B) 70-30 parts by weight of a propylene polymer; and (C) 70-150 parts by weight, based on 100 parts by weight of the components (A) and (B), of an ethylene/ alpha -olefin/non-conjugated diene copolymer rubber.