Linear evolution equations in scales of Banach spaces

Abstract

This work is devoted to the study of a class of linear time-inhomogeneous evolution equations in a scale of Banach spaces. Existence, uniquenss and stability for classical solutions is provided. We study also the associated dual Cauchy problem for which we prove uniqueness in the dual scale of Banach spaces. The results are applied to an infinite system of ordinary differential equations but also to the Fokker-Planck equation associated with the spatial logistic model in the continuum.

References in corpus (4)

• Spatial birth and death processes as solutions of stochastic equations
• Non-equilibrium dynamics for a Widom-Rowlinson type model with mutations
• Dynamical Widom-Rowlinson model and its mesoscopic limit
• Stochastic averaging principle for spatial Markov evolutions in the continuum

Cited by in corpus (3)

• The Cosmological Semiclassical Einstein Equation as an Infinite-Dimensional Dynamical System
• Stochastic averaging for a spatial population model in random environment
• Nonlinear perturbations of evolution systems in scales of Banach spaces