Existence and global behavior of solutions to fractional p-Laplacian parabolic problems
作者: Jacques GiacomoniSweta Tiwari
作者单位: 1Univ. de Pau et des Pays de l'Adour, France
2IIT 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 operatorExistence and regularity of weak solutionsAsymptotic behavior of global solutionsStabilization
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 $t\to \infty$.
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关键词翻译
关键词翻译
  • 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