2017/06/12 by Soon‐Yeong Chung, M. Choi, Chung, Soon-Yeong +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1706.03494
openalex publication_date 2017/06/12 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
The purpose of this paper is to introduce a new condition n
hbox(C)
hspace1cm
alpha
int0uf(s)ds
leq uf(u)+
betaν2+
gamma,
,
,ugt;0 for some \α, \β, \γ>0 with\n0<\β\≤ frac\(\α-2\)\λ02, where \λ0 is\nthe first eigenvalue of discrete Laplacian \Δ\ω, with which we\nobtain blow-up solutions to discrete semilinear heat equations\n\
begincasesνt
left(x,t
right)=
Delta
omegau
left(x,t
right)+f(u(x,t)), amp;\n
left(x,t
right)
in S
times
left(0,+
infty
right),
u
left(x,t
right)=0, amp;\n
left(x,t
right)
in
partial S
times
left[0,+
infty
right),
ν
left(x,0
right)=u0
geq0(nontrivial), amp; x
in
overlineS
endcases\n on a discrete network S. In fact, it will be seen that the\ncondition (C) improves the conditions known so far.\n