Maximal lp-regularity for second order non-autonomous evolution equations in umd banach spaces and application

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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 languageEnglish
Title of host publicationHandbook of Evolution Equations
PublisherNova Science Publishers, Inc.
Pages239-253
Number of pages15
ISBN (Print)9781616684297
StatePublished - 2012

Keywords

  • Lp-maximal regularity
  • Non-autonomous
  • Parabolic equations
  • Second order cauchy problem

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