Pointwise eigenfunction estimates and mean Lp-norm blowup of a system of semilinear SPDEs with symmetric Lévy generators

Eugenio Guerrero and José Alfredo López-Mimbela

Statistics & Probability Letters, 2019, vol. 149, issue C, 47-54

Abstract: We investigate semilinear systems of the form dui(t,x)=[Aiui(t,x)+Gi(u3−i(t,x))]dt+κiui(t,x)dWt,x∈D,i=1,2,with Dirichlet boundary conditions, where D⊂Rd is a bounded smooth domain, Ai is the generator of a pure-jump symmetric Lévy process in Rd, Gi is a convex locally Lipschitz function such that Gi(z)≥z1+βi for z≥0, βi>0 and κi are constants, i=1,2, and {Wt,t≥0} is a one-dimensional standard Brownian motion. We provide conditions ensuring finite-time blowup in the mean Lp-norm sense of positive weak solutions of the system above, for any p∈[1,∞). We also obtain upper bounds for the corresponding blowup times. Our approach uses in an essential way the first eigenfunctions of the generators Ai, and some two-sided estimates for them.

Keywords: Eigenfunction estimates; Green functions; Lévy measures; Symmetric Lévy process; Mean Lp-norm; Blowup of SPDEs (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167715219300215
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:149:y:2019:i:c:p:47-54

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spl.2019.01.015

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().