TY - JOUR
T1 - Generalized Solution of the First Boundary Value Problem for Parabolic Monge-Ampere Equation
JO - Journal of Partial Differential Equations
VL - 2
SP - 149
EP - 162
PY - 2001
DA - 2001/05
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5477.html
KW - Parabolic Monge-Ampère equation
KW - generalized solution
KW - convexmonotone function
KW - convex-monotone polyhedron
AB -  The existence and uniqueness of generalized solution to the first boundary value problem for parabolic Monge-Ampère equation - ut det D²_xu = f in Q = Ω × (0, T], u = φ on ∂_pQ are proved if there exists a strict generalized supersolution u_φ, where Ω ⊂ R^n is a bounded convex set, f is a nonnegative bounded measurable function defined on Q, φ ∈ C(∂_pQ), φ(x, 0) is a convex function in \overline{\Omega}, ∀x_0 ∈ ∂Ω, φ(x_0, t) ∈ C^α([0, T]).