Well-posedness and exponential decay for a laminated beam in thermoelasticity of type III with delay term

We study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III with delay term in the first equation. We show that the system is well-posed by using Lumer-Philips theorem and prove that the system is exponentially stable if and only if the wave speeds are equal.

Dynamics of stochastic retarded Benjamin-Bona-Mahony equations on unbounded channels

<p style='text-indent:20px;'>This article is devoted to the asymptotic behaviour of solutions for stochastic Benjamin-Bona-Mahony (BBM) equations with distributed delay defined on unbounded channels. We first prove the existence, uniqueness and forward compactness of pullback random attractors (PRAs). We then establish the forward asymptotic autonomy of this PRA. Finally, we study the non-delay stability of this PRA. Due to the loss of usual compact Sobolev embeddings on unbounded domains, the forward uniform tail-estimates and forward flattening of solutions are used to prove the forward asymptotic compactness of solutions.</p>

Long-time behaviour of solutions to an evolution PDE with nonstandard growth

In this paper, we prove time estimates for solutions to a general nonhomogeneous parabolic problem whose operator satisfies nonstandard growth conditions. We also study the asymptotic behaviour of solutions to an anisotropic problem.