Global solvability for the heat equation with boundary flux governed by nonlinear memory

We introduce the study of global existence and blowup in finite time for the heat equation with flux at the boundary governed by a nonlinear memory term. Via a simple transformation, the model may be written in a form which has been introduced in previous studies of tumor-induced angiogenesis. The p...

Full description

Saved in:
Bibliographic Details
Published in:Quarterly of applied mathematics 2011, Vol.69 (4), p.759-770
Main Authors: ANDERSON, JEFFREY R., DENG, KENG, DONG, ZHIHUA
Format: Article
Language:English
Subjects:
Analytical and numerical techniques
Biological and medical sciences
Boundary conditions
College mathematics
Differential equations
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Heat equation
Heat transfer
Mathematical analysis
Mathematical inequalities
Mathematics
Medical sciences
Nuclear reactors
Partial differential equations
Physics
Sciences and techniques of general use
Solid mechanics
Solvability
Structural and continuum mechanics
Tumor cell
Tumors
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Wave equations
Citations: Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We introduce the study of global existence and blowup in finite time for the heat equation with flux at the boundary governed by a nonlinear memory term. Via a simple transformation, the model may be written in a form which has been introduced in previous studies of tumor-induced angiogenesis. The present study is also in the spirit of extending work on models of the heat equation with local, nonlocal, and delay nonlinearities present in the boundary flux. Additionally, we provide a brief summary of related studies regarding heat equation models where memory terms are incorporated within reaction or diffusion.
ISSN:0033-569X
1552-4485
DOI:10.1090/S0033-569X-2011-01238-X