On the Well-Posedness for a Class of Pseudo-Differential Parabolic Equations

被引：1
|
作者：
Delgado, Julio [1 ]
机构：
[1] Imperial Coll London, Dept Math, 180 Queens Gate, London SW7 2AZ, England
来源：
INTEGRAL EQUATIONS AND OPERATOR THEORY | 2018年 / 90卷 / 01期
关键词：
Degenerate parabolic equation; Fractional diffusion; Nonhomogeneous calculus; Microlocal analysis;
D O I：
10.1007/s00020-018-2432-z
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work we study the well-posedness of the Cauchy problem for a class of pseudo-differential parabolic equations in the framework of Weyl-Hormander calculus. We establish regularity estimates, existence and uniqueness in the scale of Sobolev spaces H(m, g) adapted to the corresponding Hormander classes. Some examples are included for fractional parabolic equations and degenerate parabolic equations.
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页数：19
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