Differential and Integral Equations

Convergence to a stationary state for solutions to parabolic inverse problems of reconstruction of convolution kernels

Davide Guidetti

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Abstract

We prove the existence of solutions converging to a stationary state for abstract semilinear parabolic problems with a convolution kernel that is unknown (together with the solution). These solutions are suitable perturbations of stationary states. The main tools are maximal regularity results in an $L^1$ (time) setting. The abstract results are applied to a reaction-diffusion integrodifferential system.

Article information

Source
Differential Integral Equations Volume 20, Number 9 (2007), 961-990.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039306

Mathematical Reviews number (MathSciNet)
MR2349375

Zentralblatt MATH identifier
1212.35501

Subjects
Primary: 45K05: Integro-partial differential equations [See also 34K30, 35R09, 35R10, 47G20]
Secondary: 35K90: Abstract parabolic equations 35R30: Inverse problems 45M10: Stability theory

Citation

Guidetti, Davide. Convergence to a stationary state for solutions to parabolic inverse problems of reconstruction of convolution kernels. Differential Integral Equations 20 (2007), no. 9, 961--990. https://projecteuclid.org/euclid.die/1356039306.


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