TY - JOUR
T1 - Extended weak maximum principles for parabolic partial differential inequalities on unbounded domains
AU - Meyer, J. C.
AU - Needham, D. J.
PY - 2014/7/8
Y1 - 2014/7/8
N2 - In this paper, we establish extended maximum principles for solutions to linear parabolic partial differential inequalities on unbounded domains, where the solutions satisfy a variety of growth/decay conditions on the unbounded domain. We establish a conditional maximum principle, which states that a solution u to a linear parabolic partial differential inequality satisfies a maximum principle whenever a suitable weight function can be exhibited. Our extended maximum principles are then established by exhibiting suitable weight functions and applying the conditional maximum principle. In addition, we include several specific examples, to highlight the importance of certain generic conditions, which are required in the statements of maximum principles of this type. Furthermore, we demonstrate how to obtain associated comparison theorems from our extended maximum principles.
AB - In this paper, we establish extended maximum principles for solutions to linear parabolic partial differential inequalities on unbounded domains, where the solutions satisfy a variety of growth/decay conditions on the unbounded domain. We establish a conditional maximum principle, which states that a solution u to a linear parabolic partial differential inequality satisfies a maximum principle whenever a suitable weight function can be exhibited. Our extended maximum principles are then established by exhibiting suitable weight functions and applying the conditional maximum principle. In addition, we include several specific examples, to highlight the importance of certain generic conditions, which are required in the statements of maximum principles of this type. Furthermore, we demonstrate how to obtain associated comparison theorems from our extended maximum principles.
KW - Comparison theorems
KW - Maximum principles
KW - Parabolic partial differential equations
UR - http://www.scopus.com/inward/record.url?scp=84901280722&partnerID=8YFLogxK
U2 - 10.1098/rspa.2014.0079
DO - 10.1098/rspa.2014.0079
M3 - Article
AN - SCOPUS:84901280722
SN - 1364-5021
VL - 470
JO - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
JF - Royal Society of London. Proceedings A. Mathematical, Physical and Engineering Sciences
IS - 2167
M1 - 20140079
ER -