Abstract
AbstractWe 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.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
