GLOBAL SOLVABILITY FOR THE HEAT EQUATION WITH BOUNDARY FLUX GOVERNED BY NONLINEAR MEMORY

摘要

We introduce the study of global existence and blowup in finite time forthe heat equation with flux at the boundary governed by a nonlinear memory term. Viaa simple transformation, the model may be written in a form which has been introducedin previous studies of tumor-induced angiogenesis. The present study is also in thespirit of extending work on models of the heat equation with local, nonlocal, and delaynonlinearities present in the boundary flux. Additionally, we provide a brief summaryof related studies regarding heat equation models where memory terms are incorporatedwithin reaction or diffusion.