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Asymptotic Behavior of a Class of Nonlinear Stochastic Heat Equations with Memory Effects

Stefano Bonaccorsi, Giuseppe Da Prato, Luciano Tubaro

Type: Article

Publication Date: 2012-01-01

Citations: 17

DOI: https://doi.org/10.1137/110841795

Abstract

In this paper we investigate a class of semilinear stochastic Volterra equations which arise in the theory of heat conduction with memory effects, with dissipative nonlinearities and an additive stochastic term which models a rapidly varying external heat source. We first prove that the problem has a unique solution for all times; further, we analyze the asymptotic behavior of the solution and we prove the existence of an ergodic invariant measure.

Locations

  • Institutional Research Information System (UniversitĂ  degli Studi di Trento) - View - PDF
  • SIAM Journal on Mathematical Analysis - View

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+ Existence for Nonlinear Volterra Equations in Hilbert Spaces 1979 Viorel Barbu
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+ A general theory of heat conduction with finite wave speeds 1968 Morton E. Gurtin
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