Highly degenerate parabolic boundary value problems
Of concern are parabolic equations of the form ∂u/∂t = φ(x, ∇u)Δu (x ∈ Ω ⊂ Rn, t ≥ 0) where φ(x, ξ) > 0 on Ω X Rn but φ(x, ξ) → 0 very rapidly as X → ∂Ω. By associating the Wentzel boundary condition with this equation, the initial value problem is shown to be well-posed. This is done with the aid of the Crandall-Liggett theorem, applied in the space C(Ω). © 1989, Khayyam Publishing. All rights reserved.
Differential and Integral Equations
Goldstein, J., Lin, C., & Aftabizadeh, A. (1989). Highly degenerate parabolic boundary value problems. Differential and Integral Equations, 2 (2), 216-227. Retrieved from https://digitalcommons.memphis.edu/facpubs/4904