Scholarlink

<p>In this paper, we discuss existence and finite speed of propagation for the solutions to an initial-boundary value problem for a family of fractional thin-film equations in a bounded domain in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^d\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>d</mi> </msup> </math></EquationSource> </InlineEquation>. The nonlocal operator we consider is the spectral fractional Laplacian with Neumann boundary conditions. In the case of a “strong slippage” regime with “complete wetting” interfacial conditions, we prove local entropy estimates that entail finite speed of propagation of the support and a lower bound for the waiting time phenomenon.</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

Existence and finite speed of propagation of solutions for a multidimensional fractional thin-film equation

  • 期刊论文

  • 发表日期：

    2026年2月3日

查看全文
  • Nicola De Nitti,
  • Stefano Lisini,
  • Antonio Segatti,
  • Roman Taranets

摘要

In this paper, we discuss existence and finite speed of propagation for the solutions to an initial-boundary value problem for a family of fractional thin-film equations in a bounded domain in \(\mathbb {R}^d\) R d . The nonlocal operator we consider is the spectral fractional Laplacian with Neumann boundary conditions. In the case of a “strong slippage” regime with “complete wetting” interfacial conditions, we prove local entropy estimates that entail finite speed of propagation of the support and a lower bound for the waiting time phenomenon.