Results 11 to 20 of about 42 (41)
AxiomsThe 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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The Initial and Neumann Boundary Value Problem for a Class Parabolic Monge‐Ampère Equation
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 We consider the existence, uniqueness, and asymptotic behavior of a classical solution to the initial and Neumann boundary value problem for a class nonlinear parabolic equation of Monge‐Ampère type. We show that such solution exists for all times and is unique.
Juan Wang +3 more
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Viscosity solutions of fully nonlinear functional parabolic PDE
International Journal of Mathematics and Mathematical Sciences, Volume 2005, Issue 22, Page 3539-3550, 2005., 2005 By the technique of coupled solutions, the notion of viscosity solutions is extended to fully nonlinear retarded parabolic equations. Such equations involve many models arising from optimal control theory, economy and finance, biology, and so forth. The comparison principle is shown.
Liu Wei-an, Lu Gang
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MathematicsThe 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
MathematicsA 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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A Miyaoka–Yau inequality for hyperplane arrangements in CPn$\mathbb {CP}^n$
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract Let H$\mathcal {H}$ be a hyperplane arrangement in CPn$\mathbb {CP}^n$. We define a quadratic form Q$Q$ on RH$\mathbb {R}^{\mathcal {H}}$ that is entirely determined by the intersection poset of H$\mathcal {H}$. Using the Bogomolov–Gieseker inequality for parabolic bundles, we show that if a∈RH$\mathbf {a}\in \mathbb {R}^{\mathcal {H}}$ is ...
Martin de Borbon, Dmitri Panov
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Demonstratio MathematicaThis 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 FractionalThe 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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Well‐Posed and Ill‐Posed Boundary Value Problems for PDE 2013
, 2013 Abstract and Applied Analysis, Volume 2013, Issue 1, 2013.
Allaberen Ashyralyev +5 more
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Advances in Nonlinear AnalysisIn 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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