대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제62권1호
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  • Pages.263-274
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  • 2025
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  • 1015-8634(pISSN)
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  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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FINITE TIME SINGULARITIES FOR THE MULTIDIMENSIONAL SECOND SOUND EQUATION WITH RADIAL SYMMETRY

  • Ying Zeng (College of Teacher Education Quzhou University)
  • 투고 : 2024.03.25
  • 심사 : 2024.07.24
  • 발행 : 2025.01.31
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⟨ 이전 논문 다음 논문 ⟩

초록

We study the singularity formation of smooth solutions for the radially symmetric degenerate second sound equation, which describes the propagation of wave of temperature in superfluids. It is verified that, even for an arbitrarily small initial energy, its smooth solution may develop cusp-type singularity in the small period. The main difficulty is to prevent the occurrence of degeneracy of wave speed in a small time. Our proof is based on the method of characteristic and the energy estimate.

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과제정보

The author would also like to thank the referee for a very thorough reading and many helpful corrections and suggestions to improve the quality of the paper.

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