Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
Zbl 1098.35031
Messaoudi, Salim A.
Blow-up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation.
(English)
[J] J. Math. Anal. Appl. 320, No. 2, 902-915 (2006). ISSN 0022-247X

The nonlinear viscoelastic equation with damping and source terms, $$u_{tt}-\Delta u + \int^t_0 g(t-\tau) \delta u(\tau)d\tau + u_t\vert u_t\vert^{m-2}=u\vert u\vert^{p-2}$$ with initial conditions and Dirichlet boundary conditions is considered. The existence of local solutins is proved. For nonincreasing positive $g$ and for $p> \max(2,m),\, \max(m,p)\leq \frac{2(n-1)}{(n-2)}, \, n \geq 3,\,m>1$ the author proves that there are solutions with positive initial energy that blow up in finite time.
[Nickolaj A. Lar'kin (Maringa)]
MSC 2000:
*35B40 Asymptotic behavior of solutions of PDE
45K05 Integro-partial differential equations
35Q72 Other PDE from mechanics
74B20 Nonlinear elasticity

Keywords: blow-up; viscoelastic equations; nonlinear damping; positive initial energy; Dirichlet boundary conditions

Highlights
Master Server