Abstract
We prove well-posedness, in particular, maximal Lp-regularity for the Cauchy problem for second order abstract parabolic equations in UMD Banach spaces. Equations are non-autonomous and perturbed. Then we give application of the obtained abstract result to parabolic PDEs of second order (in the time variable) with bounded operator-valued coeffcients. This case includes, in particular, equations and a system of equations with scalar coeffcients.
| Original language | English |
|---|---|
| Title of host publication | Handbook of Evolution Equations |
| Publisher | Nova Science Publishers, Inc. |
| Pages | 239-253 |
| Number of pages | 15 |
| ISBN (Print) | 9781616684297 |
| State | Published - 2012 |
Keywords
- Lp-maximal regularity
- Non-autonomous
- Parabolic equations
- Second order cauchy problem
All Science Journal Classification (ASJC) codes
- General Mathematics