Besov maximal regularity for a class of degenerate integro‐differential equations with infinite delay in Banach spaces

Abstract

The theory of operator‐valued Fourier multipliers is used to obtain characterizations for well‐posedness of a large class of degenerate integro‐differential equations of second order in time in Banach spaces. Specifically, we treat the case of vector‐valued Besov spaces on the real line. It is important to note that in particular, the results are applicable to the more familiar scale of vector‐valued Hölder spaces. The equations under consideration are important in several applied problems in physics and material science, in particular for phenomena where memory effects are important. Several models in the area of viscoelasticity, including heat conduction and wave propagation correspond to the general class of integro‐differential equations considered here. The importance of the results is that they can be used to treat nonlinear equations.

Document Details

Document Type
Pub Defense Publication
Publication Date
Apr 28, 2020
Source ID
10.1002/mma.6462

Entities

People

  • Rafael Aparicio
  • Valentin Keyantuo

Organizations

  • Air Force Office of Scientific Research
  • University of Puerto Rico

Tags

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Graph Algorithms and Convex Optimization.

Technology Areas

  • Space