Nonlinear Evolution Equations in Scales of Banach Spaces and Applications to PDEs

  1. Jan W. Cholewa 2
  2. Carlos Quesada 1
  3. A. Rodríguez-Bernal 1
  1. 1 Departamento de Matemática Aplicada, Universidad Complutense de Madrid
  2. 2 University of Silesia
    info

    University of Silesia

    Katowice, Polonia

    ROR https://ror.org/0104rcc94

Journal:
Journal of Abstract Differential Equations and Applications

ISSN: 2158-611X

Year of publication: 2017

Volume: 8

Issue: 2

Pages: 1-69

Type: Article

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Abstract

Nonlinear evolution problems are studied by means of an abstract integral equation in a general scale of Banach spaces. The range of spaces for which a suitable notion of solution exists is analyzed. Optimal uniqueness, blow up estimates, criteria for global existence and smoothing effects of the solution are obtained. Wide applicability of the theory is illustrated by a variety of examples, involving nested and not nested scales of spaces.