Scholarlink

<p>We show the uniqueness of singular self-similar solutions to the equation <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\partial _t u = \Delta u + e^u\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>∂</mi> <mi>t</mi> </msub> <mi>u</mi> <mo>=</mo> <mi mathvariant="normal">Δ</mi> <mi>u</mi> <mo>+</mo> <msup> <mi>e</mi> <mi>u</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(x \in \textbf{R}^N\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>x</mi> <mo>∈</mo> <msup> <mi mathvariant="bold">R</mi> <mi>N</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(t &gt; 0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>&gt;</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation> with <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(N \ge 3\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>N</mi> <mo>≥</mo> <mn>3</mn> </mrow> </math></EquationSource> </InlineEquation>. We also show the convergence of regular self-similar solutions to the singular self-similar solution.</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

Uniqueness of singular self-similar solutions to the heat equation with exponential nonlinearity

  • 期刊论文

  • 发表日期：

    2025年2月28日

查看全文
  • Yūki Naito

摘要

We show the uniqueness of singular self-similar solutions to the equation \(\partial _t u = \Delta u + e^u\) ∂ t u = Δ u + e u , \(x \in \textbf{R}^N\) x ∈ R N , \(t > 0\) t > 0 with \(N \ge 3\) N ≥ 3 . We also show the convergence of regular self-similar solutions to the singular self-similar solution.