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A convergence result for the master operator
Wenxiong Chen, Yahong Guo, Congming Li +1
In this paper, we establish a convergence result for the fully fractional heat operator $\ma{s}$, also known as the master operator, stated as follows: \[\mbox{If\ }u_i\to u\ \mbox…
Monotonicity for the fractional semi-linear problem in a half space
Wenxiong Chen, Yahong Guo, Leyun Wu
In this paper, we study semilinear fractional equations in a half-space and prove that all positive solutions are strictly increasing in the -directi…
Methods in studying qualitative properties of fractional equations
Wenxiong Chen, Yahong Guo, Congming Li
In this paper, we systematically review a series of effective methods for studying the qualitative properties of solutions to fractional equations. Beginning with the pioneering ex…
Regularity of solutions for fully fractional parabolic equations
Wenxiong Chen, Yahong Guo, Congming Li
In this paper, we study the fully fractional heat equation involving the master operator: $$ (\partial_t -Δ)^{s} u(x,t) = f(x,t)\ \ \mbox{in}\ \mathbb{R}^n\times\mathbb{R} , $$ whe…
Master equations with indefinite nonlinearities
Wenxiong Chen, Yahong Guo
In this paper, we consider the following indefinite fully fractional heat equation involving the master operator \begin{equation} (\partial_t -Δ)^{s} u(x,t) = x_1u^p(x,t)\ \ \mbox{…
Liouville theorem for fully fractional master equations and its applications
Wenxiong Chen, Lingwei Ma, Yahong Guo
In this paper, we study the fully fractional master equation \begin{equation}\label{pdeq1} (\partial_t-Δ)^s u(x,t) =f(x,t,u(x,t)),\,\,(x, t)\in \mathbb{R}^n\times \mathbb{R}. \end{…