• Medientyp: Sonstige Veröffentlichung; E-Book; Bericht
  • Titel: Weak solutions to a time-dependent heat equation with nonlocal radiation boundary condition and right-hand side in $L^p$ with $pge 1$
  • Beteiligte: Druet, Pierre-Étienne [VerfasserIn]
  • Erschienen: Weierstrass Institute for Applied Analysis and Stochastics publication server, 2007
  • Sprache: Englisch
  • DOI: https://doi.org/10.20347/WIAS.PREPRINT.1253
  • Schlagwörter: 35K15 ; article ; Nonlinear parabolic equation -- nonlocal boundary condition -- right-hand side in L-p with p>=1 ; 35K55 ; 35Dxx ; 35K05
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  • Beschreibung: It is known that the time-dependent heat equation with nonlocal radiation boundary conditions possesses a unique weak solution if the heat sources are in L-2. In this paper, we generalize the known existence and uniqueness results to the case that the right-hand side belongs to an arbitrary L-p space (p >= 1). This is the continuation of the results that we recently proved for the stationary problem. The purpose of both papers is to obtain energy estimates that involve only the L-p norm of the heat sources for some exponent p close to one. Such estimates are important for the investigation of models in which the heat equation is coupled to Maxwell's equations or to the Navier-Stokes equations (dissipative heating).