Existence and global behavior of solutions to fractional p-Laplacian parabolic problems
 作者： Jacques Giacomoni,  Sweta Tiwari 作者单位： 1Univ. de Pau et des Pays de l'Adour, France2IIT Guwahati, India 刊名： Electronic Journal of Differential Equations, 2018, Vol.2018 (44,), pp.1-20 来源数据库： Directory of Open Access Journals 关键词： P-fractional operator;  Existence and regularity of weak solutions;  Asymptotic behavior of global solutions;  Stabilization; 原始语种摘要： First, we discuss the existence, the uniqueness and the regularityof the weak solution to the following parabolic equation involvingthe fractional p-Laplacian,$$\displaylines{u_t+(-\Delta)_{p}^su +g(x,u)= f(x,u)\quad \text{in } Q_T:=\Omega\times (0,T), \cru = 0 \quad \text{in } \mathbb{R}^N\setminus\Omega\times(0,T),\cru(x,0) =u_0(x)\quad \text{in }\mathbb{R}^N.}$$Next, we deal with the asymptotic behavior of global weak solutions.Precisely, we prove under additional assumptions on f and g that globalsolutions converge to the unique stationary solution as $t\to \infty$.

• global　球状的
• fractional　分级的
• Omega　希腊字母的最后一字(Ω，ω)奥米伽(导航系统)希腊字母的末一字
• Laplacian　拉普拉斯[调合]算符
• asymptotic　渐近的
• parabolic　抛物线的
• discuss　议论
• prove　实验
• operator　话务员
• behavior　行为