Abstract
We prove that the transition semigroup associated with the two phase Stefan problem is irreducible. The proof relies on a general result of approximate controllability for maximal monotone systems, see [1].
This was done during the stay in Scuola Normale Superiore di Pisa.
Partially supported by the Italian National Project MURST “Equazioni di Kolmogorov.”
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References
V. Barbu, “Analysis and control of nonlinear infinite dimensional systems”, Academic Press, San Diego, 1993.
V. Barbu and G. Da Prato, “The two phase stochastic Stefan problem”, Probab. Theory Relat. Fields, 124, 544–560, 2002.
H. Brézis, “Monotonicity methods in Hilbert spaces and some applications to nonlinear partial differential equations”, Contributions to Nonlinear Functional Analysis, E. Zarantonello, ed., Academic Press, New York, 1971.
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Barbu, V., Da Prato, G. (2005). Irreducibility of the Transition Semigroup Associated with the Two Phase Stefan Problem. In: Giannessi, F., Maugeri, A. (eds) Variational Analysis and Applications. Nonconvex Optimization and Its Applications, vol 79. Springer, Boston, MA. https://doi.org/10.1007/0-387-24276-7_11
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DOI: https://doi.org/10.1007/0-387-24276-7_11
Publisher Name: Springer, Boston, MA
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