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<p>We study an elliptic differential equation set in two habitats under semi-permeability conditions at the interface. This equation describes some dispersal process in population dynamics. Using the well-known Dore-Venni theorem, some useful results in [<CitationRef CitationID="CR6">6</CitationRef>] and [<CitationRef CitationID="CR22">22</CitationRef>], we show that the associated space operator generates an analytic semigroup in <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10884_2025_10450_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(L^{p}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mi>p</mi> </msup> </math></EquationSource> </InlineEquation>-spaces.</p>

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Semigroups Generated in \(L^{p}\)-spaces by Some Dispersal Process Including Semi-Permeability Conditions at the Interface

  • 期刊论文

  • 发表日期：

    2025年7月18日

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  • Laïd Djilali,
  • Rabah Labbas,
  • Ahmed Medeghri,
  • Abdallah Menad,
  • Alexandre Thorel

摘要

We study an elliptic differential equation set in two habitats under semi-permeability conditions at the interface. This equation describes some dispersal process in population dynamics. Using the well-known Dore-Venni theorem, some useful results in [6] and [22], we show that the associated space operator generates an analytic semigroup in \(L^{p}\) L p -spaces.