The authors study the problem of recovering a scalar memory kernel in an abstract retarded functional evolution equation of parabolic type (governed by the generator of an analytic semigroup). Results concerning existence, uniqueness, continuous dependence upon the data, and regularity are provided. Concrete examples of parabolic PDEs with delay arising in the mathematical modeling of heat flow are given.
Recovering memory kernels in retarded functional differential equations / G. Di Blasio, A. Lorenzi. - In: DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS. - ISSN 1201-3390. - 12:6(2005), pp. 837-856.
Recovering memory kernels in retarded functional differential equations
A. LorenziUltimo
2005
Abstract
The authors study the problem of recovering a scalar memory kernel in an abstract retarded functional evolution equation of parabolic type (governed by the generator of an analytic semigroup). Results concerning existence, uniqueness, continuous dependence upon the data, and regularity are provided. Concrete examples of parabolic PDEs with delay arising in the mathematical modeling of heat flow are given.
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