Abstract
Let Ω be the unit ball in R N . Consider the mean curvature equation (E0) u t = ( 1 + | Du | 2 ) σ / 2 div Du 1 + | Du | 2 + A for x ∈ Ω , t > 0 , with capillarity boundary condition (BC0) Du · γ = k ( t , u ) 1 + | Du | 2 for x ∈ ∂ Ω , t > 0 , where σ and A (⩾0) are real numbers, γ is the unit inner normal to ∂Ω and k is a smooth function with ∣ k∣ < 1. We first study the time-global existence of radial solutions of (E0)-(BC0) with some initial datum, and then study the existence, uniqueness and stability of the radial periodic traveling wave of (E0)-(BC0) when k = k( t) or k = k ˜ ( u ) is periodic.
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