An identification problem for a nonlinear evolution equation in a Banach space

Abstract

We prove the existence of a classical solution to an identification problem for a first-order semilinear differential equation in a Banach space subjected to an overdetermination expressed by means of an integral with respect to an absolutely continuous measure (with respect to the Lebesgue measure). A uniqueness and a continuity result as well as two applications to some identification problems: the first one for a parabolic equation and the second one for a hyperbolic equation are also included.

Keywords:

• identification problem
• first-order semilinear differential equation
• unknown source
• C ₀-semigroup of contractions
• parabolic equation

AMS Subject Classifications::

• Primary: 35R30
• 35L60
• Secondary: 35K20
• 35K90
• 47D06
• 47H10

Acknowledgements

The authors thank the referees for their useful comments.