Open AccessMONOTONICITY AND ASYMPTOTIC PROPERTIES OF SOLUTIONS FOR PARABOLIC EQUATIONS VIA A GIVEN INITIAL VALUE CONDITION ON GRAPHS
Author(s) -
Yiting Wu
Publication year - 2021
Publication title -
fractals
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.654
H-Index - 44
eISSN - 1793-6543
pISSN - 0218-348X
DOI - 10.1142/s0218348x21400284
Subject(s) - mathematics , monotonic function , boundary value problem , dirichlet distribution , heat equation , parabolic partial differential equation , mathematical analysis , dirichlet boundary condition , partial differential equation
In this paper, we establish several results involving the minimum and maximum principles and the comparison principles for elliptic equations and parabolic equations on finite graphs. The results are then used to prove the monotonicity and asymptotic properties of solutions for parabolic equations whose initial values are given by the equation [Formula: see text] with Dirichlet boundary conditions. Finally, an illustration with numerical experiments is provided to demonstrate our main results.