Results 1 to 10 of about 38 (38)

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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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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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 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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Unsteady Magnetohydrodynamics PDE of Monge–Ampère Type: Symmetries, Closed-Form Solutions, and Reductions

Mathematics
The paper studies an unsteady equation with quadratic nonlinearity in second derivatives, that occurs in electron magnetohydrodynamics. In mathematics, such PDEs are referred to as parabolic Monge–Ampère equations.
Andrei D. Polyanin, Alexander V. Aksenov
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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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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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Averaging Effects and Their Applications to Fractional Elliptic and Parabolic Equations

Fractal and Fractional
The averaging effect is a distinctive property possessed by fractional operators. In recent years, it has emerged as a powerful tool in the study of qualitative properties of solutions to fractional elliptic and parabolic equations.
Wenxiong Chen, Yahong Guo
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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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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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