- Tytuł:
- Global existence and blow-up phenomenon for a quasilinear viscoelastic equation with strong damping and source terms
- Autorzy:
-
Di, Huafei
Song, Zefang - Powiązania:
- https://bibliotekanauki.pl/articles/2048895.pdf
- Data publikacji:
- 2022
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
viscoelastic equation
strong damping and source
blow-up
upper and lower bound
potential well
invariant set - Opis:
- Considered herein is the global existence and non-global existence of the initial-boundary value problem for a quasilinear viscoelastic equation with strong damping and source terms. Firstly, we introduce a family of potential wells and give the invariance of some sets, which are essential to derive the main results. Secondly, we establish the existence of global weak solutions under the low initial energy and critical initial energy by the combination of the Galerkin approximation and improved potential well method involving with t. Thirdly, we obtain the finite time blow-up result for certain solutions with the non-positive initial energy and positive initial energy, and then give the upper bound for the blow-up time $T\text{}^{∗}$. Especially, the threshold result between global existence and non-global existence is given under some certain conditions. Finally, a lower bound for the life span $T\text{}^{∗}$ is derived by the means of integro-differential inequality techniques.
- Źródło:
-
Opuscula Mathematica; 2022, 42, 2; 119-155
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł