Description of the lack of compactness in Orlicz spaces and applications

الأصل · EN

In this paper, we investigate the lack of compactness of the Sobolev embedding of H¹(²) into the Orlicz space Lϕᵖ(²) associated to the function ϕₚ defined by ϕₚ(s):=eˢ²-ₖ₌₀ᵖ⁻¹ s²ᵏk!· We also undertake the study of a nonlinear wave equation with exponential growth where the Orlicz norm.ₗϕᵖ plays a crucial role. This study includes issues of global existence, scattering and qualitative study.