On a family of nonzero solutions to the heat equation \(u_t=\Delta u\) on \(\mathbb{R}^{n+1}\) which vanish on an arbitrary \(n\)-dimensional hyperplane \(P\subset\mathbb{R}^{n+1}\)

DOI10.1142/S0129167X24500307zbMATH Open1542.35212MaRDI QIDQ6563072

Dong-Ho Tsai, Chia-Hsing Nien

Publication date: 27 June 2024

Published in: International Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

heat equationCauchy problem with zero initial dataRosenbloom-Widder solutionTychonoff solution

Mathematics Subject Classification ID

Heat equation (35K05) Integral representations of solutions to PDEs (35C15) Initial value problems for second-order parabolic equations (35K15) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Cites Work

• On the oscillation behavior of solutions to the heat equation on \(\mathbb{R}^n\)
• On space-time periodic solutions of the one-dimensional heat equation
• Widder temperature representations
• A Temperature Function Which Vanishes Initially
• Expansions in Terms of Heat Polynomials and Associated Functions
• Théorèmes d'unicité pour l'équation de la chaleur.
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