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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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The method of moving planes for nonlocal uniformly fractional parabolic equations in a half space

Advances in Nonlinear Analysis
In this paper, we consider the uniformly fractional parabolic equations in a half space∂u∂t(x,t)+Dasu(x,t)=f(u(x,t)),(x,t)∈R+n×R, $$\frac{\partial u}{\partial t}\left(x,t\right)+{\mathcal{D}}_{a}^{s}u\left(x,t\right)=f\left(u\left(x,t\right)\right ...
Tang Yanjuan
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A Liouville theorem for superlinear parabolic equations on the Heisenberg group

Advanced Nonlinear Studies
We consider a parabolic nonlinear equation on the Heisenberg group. Applying the Gidas–Spruck type estimates, we prove that under suitable conditions, the equation does not have positive solutions. As an application of the nonexistence result, we provide
Wei Juncheng, Wu Ke
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On the solution stability of parabolic optimal control problems. [PDF]