We discuss the problem of establishing dissipative estimates for certain differential equations for which the usual methods apparently do not work. The main tool is a new Gronwall-type lemma with parameter. As an application, we consider a semilinear equation of viscoelasticity with low dissipation.
A Gronwall-type lemma with parameter and dissipative estimates for PDEs / Gatti, Stefania; Pata, Vittorino; Zelik, Sergey. - In: NONLINEAR ANALYSIS. - ISSN 0362-546X. - STAMPA. - 70:6(2009), pp. 2337-2343. [10.1016/j.na.2008.03.015]
A Gronwall-type lemma with parameter and dissipative estimates for PDEs
GATTI, Stefania;
2009
Abstract
We discuss the problem of establishing dissipative estimates for certain differential equations for which the usual methods apparently do not work. The main tool is a new Gronwall-type lemma with parameter. As an application, we consider a semilinear equation of viscoelasticity with low dissipation.
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