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A Liouville Theorem and Radial Symmetry for dual fractional parabolic equations
Yahong Guo, Lingwei Ma, Zhenqiu Zhang
In this paper, we first study the dual fractional parabolic equation \begin{equation*} \partial^α_t u(x,t)+(-Δ)^s u(x,t) = f(u(x,t))\ \ \mbox{in}\ \ B_1(0)\times\R , \end{equation*…
Radial symmetry and Liouville theorem for master equations
Lingwei Ma, Yahong Guo, Zhenqiu Zhang
This paper has two primary objectives. The first one is to demonstrate that the solutions of master equation \begin{equation*} (\partial_t-Δ)^s u(x,t) =f(u(x, t)), \,\,(x, t)\in B_…
Gibbons' conjecture for entire solutions of master equations
Wenxiong Chen, Lingwei Ma
In this paper, we establish a generalized version of Gibbons' conjecture in the context of the master equation \begin{equation*} (\partial_t-Δ)^s u(x,t)=f(t,u(x,t)) \,\, \mbox{in}\…
Qualitative properties of solutions for dual fractional nonlinear parabolic equations
Wenxiong Chen, Lingwei Ma
In this paper, we consider the dual fractional parabolic problem in the right half space. We prove that the positive solutions are strictly increasing in direction without as…