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Volume 14, Issue 2
Generalized Solution of the First Boundary Value Problem for Parabolic Monge-Ampere Equation

Li Chen , Guanglie Wang & Songzhe Lian

J. Part. Diff. Eq., 14 (2001), pp. 149-162.

Published online: 2001-05

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  • Abstract
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]).
  • Keywords

Parabolic Monge-Ampère equation generalized solution convexmonotone function convex-monotone polyhedron

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@Article{JPDE-14-149, author = {Li Chen , Guanglie Wang and Songzhe Lian }, title = {Generalized Solution of the First Boundary Value Problem for Parabolic Monge-Ampere Equation}, journal = {Journal of Partial Differential Equations}, year = {2001}, volume = {14}, number = {2}, pages = {149--162}, abstract = { 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]).}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5477.html} }
TY - JOUR T1 - Generalized Solution of the First Boundary Value Problem for Parabolic Monge-Ampere Equation AU - Li Chen , Guanglie Wang & Songzhe Lian 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]).
Li Chen , Guanglie Wang and Songzhe Lian . (2001). Generalized Solution of the First Boundary Value Problem for Parabolic Monge-Ampere Equation. Journal of Partial Differential Equations. 14 (2). 149-162. doi:
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