Singular nonlinear parabolic boundary value problems in one space dimension


Global existence and uniqueness are established for the mixed initial-boundary problem for the nonlinear parabolic equation ∂u ∂t = φ(x, ∂u ∂x) ∂2u ∂x2 (0 ≤ x ≤ 1, t ≤ 0), where φ(x, ξ) ≥φ0(x) > 0 for 0 < x < 1 and ∝01 φ0(x)-1 dx < ∞. The boundary conditions can be either linear (e.g., Dirichlet, Neumann, or periodic) or nonlinear, in which case they take the form (- 1)j u(j, t) ε{lunate} βj(ux(J, t)) for j = 0, 1, where βj is a maximal monotone graph in R × R containing the origin. © 1987.

Publication Title

Journal of Differential Equations