Abstract functional differential equations and reaction-diffusion systems

R. H. Martin, Hal Smith

Research output: Contribution to journalArticle

353 Citations (Scopus)

Abstract

Several fundamental results on the existence and behavior of solutions to semilinear functional differential equations are developed in a Banach space setting. The ideas are applied to reaction-diffusion systems that have time delays in the nonlinear reaction terms. The techniques presented here include differential inequalities, invariant sets, and Lyapunov functions, and therefore they provide for a wide range of applicability. The results on inequalities and especially strict inequalities are new even in the context of semi linear equations whose nonlinear terms do not contain delays.

Original languageEnglish (US)
Pages (from-to)1-44
Number of pages44
JournalTransactions of the American Mathematical Society
Volume321
Issue number1
DOIs
StatePublished - 1990

Fingerprint

Abstract Differential Equations
Banach spaces
Lyapunov functions
Functional Differential Equations
Linear equations
Reaction-diffusion System
Time delay
Differential equations
Semilinear Differential Equations
Semilinear Equations
Differential Inequalities
Term
Invariant Set
Behavior of Solutions
Lyapunov Function
Existence of Solutions
Time Delay
Banach space
Range of data
Context

Keywords

  • Differential inequalities
  • Invariant sets
  • Reaction-diffusion-delay systems
  • Semilinear functional differential equations

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Abstract functional differential equations and reaction-diffusion systems. / Martin, R. H.; Smith, Hal.

In: Transactions of the American Mathematical Society, Vol. 321, No. 1, 1990, p. 1-44.

Research output: Contribution to journalArticle

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