Exponential decay and blow-up results for a nonlinear heat equation with a viscoelastic term and Robin conditions
Annales Polonici Mathematici, Tome 119 (2017) no. 2, pp. 121-145
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We consider a nonlinear heat equation with a viscoelastic term and Robin conditions. First, we prove existence and uniqueness of a weak solution. Next, we prove that any weak solution with negative initial energy will blow up in finite time. Finally, we give a sufficient condition for the global existence and exponential decay of weak solutions. The main tools are the Faedo–Galerkin method and defining a modified energy functional together with the technique of Lyapunov functional.
Keywords:
consider nonlinear heat equation viscoelastic term robin conditions first prove existence uniqueness weak solution prove weak solution negative initial energy blow finite time finally sufficient condition global existence exponential decay weak solutions main tools faedo galerkin method defining modified energy functional together technique lyapunov functional
Affiliations des auteurs :
Nguyen Thanh Long 1 ; Nguyen Van Y 2 ; Le Thi Phuong Ngoc 3
@article{10_4064_ap4084_3_2017,
author = {Nguyen Thanh Long and Nguyen Van Y and Le Thi Phuong Ngoc},
title = {Exponential decay and blow-up results for a nonlinear heat equation with a viscoelastic term and {Robin} conditions},
journal = {Annales Polonici Mathematici},
pages = {121--145},
publisher = {mathdoc},
volume = {119},
number = {2},
year = {2017},
doi = {10.4064/ap4084-3-2017},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap4084-3-2017/}
}
TY - JOUR AU - Nguyen Thanh Long AU - Nguyen Van Y AU - Le Thi Phuong Ngoc TI - Exponential decay and blow-up results for a nonlinear heat equation with a viscoelastic term and Robin conditions JO - Annales Polonici Mathematici PY - 2017 SP - 121 EP - 145 VL - 119 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.4064/ap4084-3-2017/ DO - 10.4064/ap4084-3-2017 LA - en ID - 10_4064_ap4084_3_2017 ER -
%0 Journal Article %A Nguyen Thanh Long %A Nguyen Van Y %A Le Thi Phuong Ngoc %T Exponential decay and blow-up results for a nonlinear heat equation with a viscoelastic term and Robin conditions %J Annales Polonici Mathematici %D 2017 %P 121-145 %V 119 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.4064/ap4084-3-2017/ %R 10.4064/ap4084-3-2017 %G en %F 10_4064_ap4084_3_2017
Nguyen Thanh Long; Nguyen Van Y; Le Thi Phuong Ngoc. Exponential decay and blow-up results for a nonlinear heat equation with a viscoelastic term and Robin conditions. Annales Polonici Mathematici, Tome 119 (2017) no. 2, pp. 121-145. doi: 10.4064/ap4084-3-2017
Cité par Sources :