On semilinear Cauchy problems with non-dense domain

Pierre Magal, Shigui Ruan

Research output: Contribution to journalArticle

51 Citations (Scopus)

Abstract

We are interested in studying semilinear Cauchy problems in which the closed linear operator is not Hille-Yosida and its domain is not densely defined. Using integrated semigroup theory, we study the positivity of solutions to the semilinear problem, the Lipschitz perturbation of the problem, diffierentiability of the solutions with respect to the state variable, time diffierentiability of the solutions, and the stability of equilibria. The obtained results can be used to study several types of differential equations, including delay diffierential equations, age-structure models in population dynamics, and evolution equations with nonlinear boundary conditions.

Original languageEnglish (US)
Pages (from-to)1041-1084
Number of pages44
JournalAdvances in Differential Equations
Volume14
Issue number11-12
StatePublished - 2009

Fingerprint

Semilinear
Cauchy Problem
Integrated Semigroups
Age Structure
Closed Operator
Population dynamics
Semigroup Theory
Stability of Equilibria
Delay Equations
Nonlinear Boundary Conditions
Model structures
Population Dynamics
Dynamic Equation
Positivity
Linear Operator
Evolution Equation
Lipschitz
Differential equations
Boundary conditions
Differential equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

On semilinear Cauchy problems with non-dense domain. / Magal, Pierre; Ruan, Shigui.

In: Advances in Differential Equations, Vol. 14, No. 11-12, 2009, p. 1041-1084.

Research output: Contribution to journalArticle

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