user

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.
引用
收藏
页数：19
相关论文
共 50 条
  • [11] Well-posedness of fractional parabolic equations
    Ashyralyev, Allaberen
    BOUNDARY VALUE PROBLEMS, 2013, : 1 - 18
  • [12] Well-posedness of fractional parabolic equations
    Allaberen Ashyralyev
    Boundary Value Problems, 2013
  • [13] Well-posedness and longtime dynamics for the finitely degenerate parabolic and pseudo-parabolic equations
    Liu, Gongwei
    Tian, Shuying
    JOURNAL OF EVOLUTION EQUATIONS, 2024, 24 (01)
  • [14] Well-posedness and longtime dynamics for the finitely degenerate parabolic and pseudo-parabolic equations
    Gongwei Liu
    Shuying Tian
    Journal of Evolution Equations, 2024, 24
  • [15] Well-posedness of delay parabolic difference equations
    Allaberen Ashyralyev
    Deniz Agirseven
    Advances in Difference Equations, 2014
  • [16] Well-posedness of the Cauchy problem for p-evolution systems of pseudo-differential operators
    Ascanelli, Alessia
    Boiti, Chiara
    JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 2013, 4 (02) : 113 - 143
  • [17] Well-posedness for parabolic equations of arbitrary order
    Marchi, C
    ASYMPTOTIC ANALYSIS, 2003, 35 (01) : 41 - 64
  • [18] Well-posedness of delay parabolic difference equations
    Ashyralyev, Allaberen
    Agirseven, Deniz
    ADVANCES IN DIFFERENCE EQUATIONS, 2014,
  • [19] On the well-posedness of a nonlinear pseudo-parabolic equation
    Nguyen Huy Tuan
    Vo Van Au
    Vo Viet Tri
    Donal O’Regan
    Journal of Fixed Point Theory and Applications, 2020, 22
  • [20] On the well-posedness of a nonlinear pseudo-parabolic equation
    Tuan, Nguyen Huy
    Au, Vo Van
    Tri, Vo Viet
    O'Regan, Donal
    JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2020, 22 (03)
12345