Results 1 to 10 of about 56,235 (88)

The first initial-boundary value problem of parabolic Monge–Ampère equations outside a bowl-shaped domain

Boundary Value Problems, 2021
In this paper, we study the parabolic Monge–Ampère equations − u t det ( D 2 u ) = g $-u_{t}\det (D^{2}u)=g$ outside a bowl-shaped domain with g being the perturbation of g 0 ( | x | ) $g_{0}(|x|)$ at infinity.
Limei Dai, Huihui Cheng
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Numerical solutions to two-dimensional fourth order parabolic thin film equations using the Parabolic Monge-Ampere method

AIMS Mathematics, 2023
This article presents the Parabolic-Monge-Ampere (PMA) method for numerical solutions of two-dimensional fourth-order parabolic thin film equations with constant flux boundary conditions.
Abdulghani R. Alharbi
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Entire Solutions of Cauchy Problem for Parabolic Monge–Ampère Equations

Advanced Nonlinear Studies, 2020
In this paper, we study the Cauchy problem of the parabolic Monge–Ampère ...
Dai Limei, Bao Jiguang
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The Maximal Regularity of Nonlocal Parabolic Monge–Ampère Equations and Its Monotonicity in the Whole Space

Axioms
The Monge–Ampère operator, as a nonlinear operator embedded in parabolic differential equations, complicates the demonstration of maximal regularity for these equations.
Xingyu Liu
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A Note on the Asymptotic Behavior of Parabolic Monge-Ampère Equations on Riemannian Manifolds

Journal of Applied Mathematics, 2013
We study the asymptotic behavior of the parabolic Monge-Ampère equation in , in , where is a compact complete Riemannian manifold, λ is a positive real parameter, and is a smooth function.
Qiang Ru
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The Sinkhorn algorithm, parabolic optimal transport and geometric Monge–Ampère equations [PDF]

Numerische Mathematik, 2017
We show that the discrete Sinkhorn algorithm—as applied in the setting of Optimal Transport on a compact manifold—converges to the solution of a fully non-linear parabolic PDE of Monge–Ampère type, in a large-scale limit.
R. Berman
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Some applications and maximum principles for multi-term time-space fractional parabolic Monge-Ampère equation

Demonstratio Mathematica
This study first establishes several maximum and minimum principles involving the nonlocal Monge-Ampère operator and the multi-term time-space fractional Caputo-Fabrizio derivative.
Guan Tingting, Wang Guotao, Araci Serkan
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Qualitative properties of solutions for dual fractional parabolic equations involving nonlocal Monge-Ampère operator

Advances in Nonlinear Analysis
In this article, we mainly study the qualitative properties of solutions for dual fractional-order parabolic equations with nonlocal Monge-Ampère operators in different domains ∂tβμ(y,t)−Dατμ(y,t)=f(μ(y,t)).{\partial }_{t}^{\beta }\mu \left(y,t)-{D}_ ...
Yang Zerong, He Yong
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Symmetries, Reductions and Exact Solutions of Nonstationary Monge–Ampère Type Equations

Mathematics
A family of strongly nonlinear nonstationary equations of mathematical physics with three independent variables is investigated, which contain an arbitrary degree of the first derivative with respect to time and a quadratic combination of second ...
Alexander V. Aksenov, Andrei D. Polyanin
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Monotonicity of solutions for parabolic equations involving nonlocal Monge-Ampère operator

Advances in Nonlinear Analysis
In this article, we consider the parabolic equations with nonlocal Monge-Ampère operators ∂u∂t(x,t)−Dsθu(x,t)=f(u(x,t)),(x,t)∈R+n×R.\frac{\partial u}{\partial t}\left(x,t)-{D}_{s}^{\theta }u\left(x,t)=f\left(u\left(x,t)),\hspace{1.0em}\left(x,t)\in ...
Du Guangwei, Wang Xinjing
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