Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840010 | Nonlinear Analysis: Theory, Methods & Applications | 2014 | 11 Pages |
Abstract
We establish an existence, uniqueness and continuous dependence result for the weak solutions to the nonlinear viscoelastic equation with hereditary memory on a bounded three-dimensional domain |∂tu|ρ∂ttu−Δ∂ttu+γ(−Δ)θ∂tu−αΔu+∫0∞μ(s)Δu(t−s)ds+f(u)=h with Dirichlet boundary conditions. In particular, the parameter ρρ belongs to the interval [0,4][0,4], the value 4 being critical for the Sobolev embeddings, while ff can reach the critical polynomial order 5.
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Authors
Monica Conti, Elsa M. Marchini, Vittorino Pata,