Gradient blow-up solution with small initial datum for a Hamilton-Jacobi equation with degenerate diffusion

摘要

We study the gradient blow-up phenomena for a Hamilton-Jacobi equation with degenerate diffusion u(t) = (vertical bar u(x)vertical bar(p-2)u(x))(x) + vertical bar u(x)vertical bar(q) in an interval for q p = 2. In the main theorem, we construct a gradient blow-up solution with a small L-1 initial datum. (C) 2018 Elsevier Inc. All rights reserved.