No abstract

In this paper we consider an n-dimensional system of thermoelasticity, where a viscoelastic dissipation is acting on a part of the boundary. By using a lemma, first appeared in the work of Messaoudi and Soufyane [“General decay of solutions of a wave equation with a boundary control of memory type,” Nonlinear Anal.: Real World Appl. (to be published)], we establish a general decay result, from which the usual exponential and polynomial decay are only special cases. Our result improves earlier ones in the literature and extends the general result of Messaoudi and Soufyane [“General decay of solutions of a wave equation with a boundary control of memory type,” Nonlinear Anal.: Real World Appl. 11, 2896 (2010] to thermoelastic systems.

In this paper we consider an n-dimensional system of visco-thermoelasticity with second sound, where a viscoelastic dissipation is acting on a part of the boundary. We prove some decay results for solutions with specific regular initial data. In this regard, polynomial and general decay results are established.

In this work, we study the fractional Laplacian equation with singular nonlinearity: [Formula: see text] where [Formula: see text] is a bounded domain in [Formula: see text] with smooth boundary [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] [Formula: see text] [Formula: see text] is the fractional Sobolev exponent, [Formula: see text] are two parameters, [Formula: see text] are nonnegative weight functions, and [Formula: see text] is the fractional Laplace operator. We use the Nehari manifold approach and some variational techniques in order to show the existence and multiplicity of positive solutions of the above problem with respect to the parameter [Formula: see text] and [Formula: see text].

In this paper, we consider a multi-dimensional system of thermoelasticity type III with a viscoelastic damping acting on a part of the boundary. We establish a general decay result, from which the usual exponential and polynomial decay rates are only special cases. (2000). 35B37 · 35L55 · 74D05 · 93D15 · 93D20. Mathematics Subject Classification