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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2016-12-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2016/332/abstr.html |
| Summary: | 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. |
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| ISSN: | 1072-6691 |