5 papers
An Observation About Weak Solutions of Linear Differential Equations in Hilbert Spaces
Vittorino Pata, Justin T. Webster
In this note we propose a definition of weak solution for an abstract Cauchy problem in a Hilbert space, and we discuss existence and uniqueness results.
Abstract damped wave equations: The optimal decay rate
Filippo Dell'Oro, Lorenzo Liverani, Vittorino Pata
The exponential decay rate of the semigroup generated by the abstract damped wave equation is here addressed, where is…
A hierarchy of heat conduction laws
Filippo Dell'Oro, Vittorino Pata
The purpose of this work is to produce a family of equations describing the evolution of the temperature in a rigid heat conductor. This is obtained by means of successive approxim…
Steady states of elastically-coupled extensible double-beam systems
Filippo Dell'Oro, Claudio Giorgi, Vittorino Pata
Given and , we analyze an abstract version of the nonlinear stationary model in dimensionless form $$\begin{cases} u"" - \Big(β+ \varrho\int_0^1 |u'(s…
Exponential attractors for abstract equations with memory and applications to viscoelasticity
Valeria Danese, Pelin G. Geredeli, Vittorino Pata
We consider an abstract equation with memory of the form $$\partial_t \boldsymbol{x}(t)+\int_{0}^\infty k(s) \boldsymbol{A}\boldsymbol{x}(t-s){\rm d} s+\boldsymbol{B}\boldsymbol{x}…