Geodesic
On the p-Laplacian type equation with logarithmic nonlinearity: existence, decay and blow up
Filomat, Tome 37 (2023) no. 16, p. 5485

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

DOI

This work is deal with a problem of wave equation with p-Laplacian, strong damping and logarithmic source terms under initial-boundary conditions. The global existence of weak solution was proved for related to the equation. Global existence results of solutions are obtained using the potential well method, Galerkin method and compactness approach corresponding to the logarithmic source term. Besides, we established the energy functional decaying polynomially to zero as the time goes to infinity due to Nakao's inequality and some precise priori estimates on logarithmic nonlinearity. For suitable conditions we proved the finite time blow up results of solutions. The proof is based on the concavity method, perturbation energy method and differential–integral inequality technique. Additionally, under suitable assumptions on initial data, the infinite time blow up result is investigated with negative initial energy.
DOI : 10.2298/FIL2316485I
Classification : 35B44, 35A01, 35B40, 35G60, 35L05
Keywords: Blow up, Boundary value problem, Global existence, Partial differential equation, Polynomial decay, p-Laplacian equation, Logarithmic nonlinearity 
Nazlı Irkıl. On the p-Laplacian type equation with logarithmic nonlinearity: existence, decay and blow up. Filomat, Tome 37 (2023) no. 16, p. 5485 . doi: 10.2298/FIL2316485I
@article{10_2298_FIL2316485I,
     author = {Nazl{\i} Irk{\i}l},
     title = {On the {p-Laplacian} type equation with logarithmic nonlinearity: existence, decay and blow up},
     journal = {Filomat},
     pages = {5485 },
     year = {2023},
     volume = {37},
     number = {16},
     doi = {10.2298/FIL2316485I},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2316485I/}
}
TY  - JOUR
AU  - Nazlı Irkıl
TI  - On the p-Laplacian type equation with logarithmic nonlinearity: existence, decay and blow up
JO  - Filomat
PY  - 2023
SP  - 5485 
VL  - 37
IS  - 16
UR  - http://geodesic.mathdoc.fr/articles/10.2298/FIL2316485I/
DO  - 10.2298/FIL2316485I
LA  - en
ID  - 10_2298_FIL2316485I
ER  - 
%0 Journal Article
%A Nazlı Irkıl
%T On the p-Laplacian type equation with logarithmic nonlinearity: existence, decay and blow up
%J Filomat
%D 2023
%P 5485 
%V 37
%N 16
%U http://geodesic.mathdoc.fr/articles/10.2298/FIL2316485I/
%R 10.2298/FIL2316485I
%G en
%F 10_2298_FIL2316485I

Cité par Sources :