Details

Autor(en) / Beteiligte

• Knops, Robin J.
• Quintanilla, Ramon

Titel

Asymptotic spatial behavior for the heat equation on noncompact regions

Ist Teil von

• Studies in applied mathematics (Cambridge), 2024-01

Erscheinungsjahr

2024

Link zum Volltext

Quelle

Wiley Blackwell Single Titles

Beschreibungen/Notizen

• Abstract We consider the isotropic initial boundary value problem for the heat equation on open regions with noncompact boundary and construct differential inequalities for a generalized heat flow measure defined over a spherical cross section. Under suitable assumptions, integration of the differential inequality leads to spatial growth and decay rate estimates for mean‐square cross‐sectional measures of the time‐weighted temperature spatial gradient. The estimates are then used to obtain similar results for the time‐weighted temperature. In particular, when the base heat flow measure is positive, the time‐weighted temperature becomes pointwise unbounded at large spatial distance.