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An identification problem for a semilinear evolution delay equation
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Published/Copyright:
November 27, 2013
Abstract.
We prove the existence, uniqueness and continuous dependence on the data of a mild solution to an identification problem for a first-order semilinear delay 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). Two applications to some identification problems, the first one for a parabolic delay equation and the second one for a hyperbolic delay equation, are also considered.
Keywords: Identification problem; first-order semilinear differential delay equation; unknown source; C0-semigroup of contractions; parabolic equation; first order hyperbolic equation
Received: 2013-3-20
Published Online: 2013-11-27
Published in Print: 2014-4-1
© 2014 by Walter de Gruyter Berlin/Boston
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- Frontmatter
- Obituary of Alfredo Lorenzi
- A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
- Reconstruction of interfaces using CGO solutions for the Maxwell equations
- An identification problem for a semilinear evolution delay equation
- On determining an absorption coefficient and a speed of sound in the wave equation by the BC method
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Articles in the same Issue
- Frontmatter
- Obituary of Alfredo Lorenzi
- A Fourier truncated regularization method for a Cauchy problem of a semi-linear elliptic equation
- Reconstruction of interfaces using CGO solutions for the Maxwell equations
- An identification problem for a semilinear evolution delay equation
- On determining an absorption coefficient and a speed of sound in the wave equation by the BC method
- Convergence of posteriors for structurally non-identified problems using results from the theory of inverse problems
- A comparison of regularization methods for identifying unknown source problem for the modified Helmholtz equation
