Abstract
The author proves well posedness and maximal Lp
regularity for the Cauchy problem for second order abstract parabolic equations in UMD Banach spaces. Such kind of subject was already studied by Arendt, Chill, Fornaro, Poupaud and Srivastava; but the approach followed in this paper allows to the author to handle, for the first time, with non-autonomous and perturbed equations. Lastly the author gives an application in the case of a parabolic PDE of second order (in time variables).
regularity for the Cauchy problem for second order abstract parabolic equations in UMD Banach spaces. Such kind of subject was already studied by Arendt, Chill, Fornaro, Poupaud and Srivastava; but the approach followed in this paper allows to the author to handle, for the first time, with non-autonomous and perturbed equations. Lastly the author gives an application in the case of a parabolic PDE of second order (in time variables).
| Original language | English |
|---|---|
| Pages (from-to) | 379-393 |
| Number of pages | 15 |
| Journal | International journal of evolution equations |
| Volume | 3 |
| Issue number | 3 |
| State | Published - 2009 |
Keywords
- 35K90
- 35K20