Scholarlink

<p>We provide conditions under which we prove for measure-valued transport equations with non-linear reaction term in the space of finite signed Radon measures, that positivity is preserved, as well as absolute continuity with respect to Lebesgue measure, if the initial condition has that property. Moreover, if the initial condition has <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13324_2025_1093_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> regular density, then the solution has the same property.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Invariance properties of the solution operator for measure-valued semilinear transport equations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年6月22日

查看全文
  • Sander C. Hille,
  • Rainey Lyons,
  • Adrian Muntean

摘要

We provide conditions under which we prove for measure-valued transport equations with non-linear reaction term in the space of finite signed Radon measures, that positivity is preserved, as well as absolute continuity with respect to Lebesgue measure, if the initial condition has that property. Moreover, if the initial condition has \(L^p\) L p regular density, then the solution has the same property.