Heat Equation with Inverse-Square Potential of Bridging Type Across Two Half-Lines - Archive ouverte HAL
Communication Dans Un Congrès Année : 2022

Heat Equation with Inverse-Square Potential of Bridging Type Across Two Half-Lines

Résumé

The heat equation with inverse-square potential on both half-lines of R is discussed in the presence of bridging boundary conditions at the origin. The problem is the lowest energy (zero-momentum) mode of the transmission of the heat flow across a Grushin-type cylinder, a generalisation of an almost-Riemannian structure with compact singularity set. This and related models are reviewed, and the issue is posed of the analysis of the dispersive properties for the heat kernel generated by the underlying positive self-adjoint operator. Numerical integration is shown that provides a first insight and relevant qualitative features of the solution at later times.

Dates et versions

hal-04309754 , version 1 (27-11-2023)

Identifiants

Citer

Matteo Gallone, Alessandro Michelangeli, Eugenio Pozzoli. Heat Equation with Inverse-Square Potential of Bridging Type Across Two Half-Lines. Qualitative Properties of Dispersive PDEs, INdAM, 2021, Bari, Italy. pp.141-164, ⟨10.1007/978-981-19-6434-3_7⟩. ⟨hal-04309754⟩
9 Consultations
0 Téléchargements

Altmetric

Partager

More