Blow-up of solutions for viscoelastic equations of Kirchhoff type with arbitrary positive initial energy
We consider the viscoelastic equation $$ u_{tt}(x,t)-M(\|\nabla u\|_2^2) \Delta u(x,t)+\int_0^t g(t-s)\Delta u(x,s)ds+u_t =|u|^{p-1}u $$ with suitable initial data and boundary conditions. Under certain assumptions on the kernel $g$ and the initial data, we establish a new blow-up result for...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-12-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/332/abstr.html |
| id |
doaj-ef28ca311e94401abf094397eebda0e2 |
|---|---|
| record_format |
Article |
| spelling |
doaj-ef28ca311e94401abf094397eebda0e22020-11-24T22:51:49ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912016-12-012016332,18Blow-up of solutions for viscoelastic equations of Kirchhoff type with arbitrary positive initial energyZhifeng Yang0Zhaogang Gong1 Hengyang Normal Univ., China Hengyang Normal Univ., China We consider the viscoelastic equation $$ u_{tt}(x,t)-M(\|\nabla u\|_2^2) \Delta u(x,t)+\int_0^t g(t-s)\Delta u(x,s)ds+u_t =|u|^{p-1}u $$ with suitable initial data and boundary conditions. Under certain assumptions on the kernel $g$ and the initial data, we establish a new blow-up result for arbitrary positive initial energy, by using simple analysis techniques.http://ejde.math.txstate.edu/Volumes/2016/332/abstr.htmlViscoelastic equationblow-uparbitrary positive initial energy |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Zhifeng Yang Zhaogang Gong |
| spellingShingle |
Zhifeng Yang Zhaogang Gong Blow-up of solutions for viscoelastic equations of Kirchhoff type with arbitrary positive initial energy Electronic Journal of Differential Equations Viscoelastic equation blow-up arbitrary positive initial energy |
| author_facet |
Zhifeng Yang Zhaogang Gong |
| author_sort |
Zhifeng Yang |
| title |
Blow-up of solutions for viscoelastic equations of Kirchhoff type with arbitrary positive initial energy |
| title_short |
Blow-up of solutions for viscoelastic equations of Kirchhoff type with arbitrary positive initial energy |
| title_full |
Blow-up of solutions for viscoelastic equations of Kirchhoff type with arbitrary positive initial energy |
| title_fullStr |
Blow-up of solutions for viscoelastic equations of Kirchhoff type with arbitrary positive initial energy |
| title_full_unstemmed |
Blow-up of solutions for viscoelastic equations of Kirchhoff type with arbitrary positive initial energy |
| title_sort |
blow-up of solutions for viscoelastic equations of kirchhoff type with arbitrary positive initial energy |
| publisher |
Texas State University |
| series |
Electronic Journal of Differential Equations |
| issn |
1072-6691 |
| publishDate |
2016-12-01 |
| description |
We consider the viscoelastic equation
$$
u_{tt}(x,t)-M(\|\nabla u\|_2^2) \Delta u(x,t)+\int_0^t
g(t-s)\Delta u(x,s)ds+u_t =|u|^{p-1}u
$$
with suitable initial data and boundary conditions.
Under certain assumptions on the kernel $g$ and the initial data,
we establish a new blow-up result for arbitrary positive initial energy,
by using simple analysis techniques. |
| topic |
Viscoelastic equation blow-up arbitrary positive initial energy |
| url |
http://ejde.math.txstate.edu/Volumes/2016/332/abstr.html |
| work_keys_str_mv |
AT zhifengyang blowupofsolutionsforviscoelasticequationsofkirchhofftypewitharbitrarypositiveinitialenergy AT zhaoganggong blowupofsolutionsforviscoelasticequationsofkirchhofftypewitharbitrarypositiveinitialenergy |
| _version_ |
1725668610144206848 |