ELLIPTIC AND PARABOLIC EQUATIONS WITH FRACTIONAL DIFFUSION AND DYNAMIC BOUNDARY CONDITIONS

被引：32
|
作者：
Gal, Ciprian G. [1 ]
Warma, Mahamadi [2 ]
机构：
[1] Florida Int Univ, Dept Math, Miami, FL 33199 USA
[2] Univ Puerto Rico, Dept Math, Rio Piedras Campus POB 70377, San Juan, PR 00936 USA
来源：
EVOLUTION EQUATIONS AND CONTROL THEORY | 2016年 / 5卷 / 01期
关键词：
The fractional Laplace operator; fractional Wentzell boundary conditions; global attractor; exponential attractor; semilinear reaction-diffusion equation; elliptic problem; fractional Steklov operator; fractional Dirichlet-to-Neumann operator; NONLOCAL VECTOR CALCULUS;
D O I：
10.3934/eect.2016.5.61
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We investigate a class of semilinear parabolic and elliptic problems with fractional dynamic boundary conditions. We introduce two new operators, the so-called fractional Wentzell Laplacian and the fractional Steklov operator, which become essential in our study of these nonlinear problems. Besides giving a complete characterization of well-posedness and regularity of bounded solutions, we also establish the existence of finite-dimensional global attractors and also derive basic conditions for blow-up.
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页码：61 / 103
页数：43
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