Articles written in Proceedings – Mathematical Sciences

    • Containment of c0 and ℓ1 in π1(E, F)

      Mohsen Alimohammady

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      Suppose π1(E, F) is the space of all absolutely 1-summing operators between two Banach spacesE andF. We show that ifF has a copy of c0, then π1 (E, F) will have a copy of c0, and under some conditions ifE has a copy of ℓ1 then π1 (E, F) would have a complemented copy of ℓ1.

    • Blow up property for viscoelastic evolution equations on manifolds with conical degeneration


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      This paper is concerned with the study of nonlinear viscoelastic evolutionequation with strong damping and source terms, described by $$u_{tt} − \Delta_{\mathbb{B}}u +\int^{t}_{0}\,g(t − \tau)\Delta_{\mathbb{B}}u(\tau)d\tau + f (x)u_{t} |u_{t}|^{m−2}\\ = h(x)|u|^{p−2}u, \,\,\,\,x \in int\,\mathbb{B}, t > 0,$$

      where $\mathbb{B}$ is a stretched manifold. First, we prove the solutions of problem (1.1) in the cone Sobolev space $\mathcal{H}^{1,\frac{n}{2}}_{2,0} (\mathbb{B})$, which admit a blow up in finite time for $p$ > $m$ and positive initial energy. Then, we construct a lower bound for obtaining blow up time under appropriate assumptions on data.

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