Parabolic Equations

Pierre Magal, Shigui Ruan

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The theories developed in the previous chapters can be used to study some parabolic equations as well. In this chapter, we first consider linear abstract Cauchy problems with non-densely defined and almost sectorial operators; that is, the part of this operator in the closure of its domain is sectorial. Such problems naturally arise for parabolic equations with nonhomogeneous boundary conditions. By using the integrated semigroup theory, we prove an existence and uniqueness result for integrated solutions. Moreover, we study the linear perturbation problem. Then in the second section we provide detailed stability and bifurcation analyses for a scalar reaction-diffusion equation, namely, a size-structured model.

Original languageEnglish (US)
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages451-521
Number of pages71
DOIs
StatePublished - Jan 1 2018

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume201
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Fingerprint

Parabolic Equation
Boundary conditions
Integrated Semigroups
Sectorial Operator
Abstract Cauchy Problem
Nonhomogeneous Boundary Conditions
Semigroup Theory
Existence and Uniqueness Results
Reaction-diffusion Equations
Closure
Bifurcation
Scalar
Perturbation
Operator
Model

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

Magal, P., & Ruan, S. (2018). Parabolic Equations. In Applied Mathematical Sciences (Switzerland) (pp. 451-521). (Applied Mathematical Sciences (Switzerland); Vol. 201). Springer. https://doi.org/10.1007/978-3-030-01506-0_9

Parabolic Equations. / Magal, Pierre; Ruan, Shigui.

Applied Mathematical Sciences (Switzerland). Springer, 2018. p. 451-521 (Applied Mathematical Sciences (Switzerland); Vol. 201).

Research output: Chapter in Book/Report/Conference proceedingChapter

Magal, P & Ruan, S 2018, Parabolic Equations. in Applied Mathematical Sciences (Switzerland). Applied Mathematical Sciences (Switzerland), vol. 201, Springer, pp. 451-521. https://doi.org/10.1007/978-3-030-01506-0_9
Magal P, Ruan S. Parabolic Equations. In Applied Mathematical Sciences (Switzerland). Springer. 2018. p. 451-521. (Applied Mathematical Sciences (Switzerland)). https://doi.org/10.1007/978-3-030-01506-0_9
Magal, Pierre ; Ruan, Shigui. / Parabolic Equations. Applied Mathematical Sciences (Switzerland). Springer, 2018. pp. 451-521 (Applied Mathematical Sciences (Switzerland)).
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