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Recovering a scalar time dependent function in a multidimensional parabolic equation by a nonlocal boundary additional information
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U. Fedus'
Veröffentlicht/Copyright:
11. September 2008
Abstract
In this paper we solve (locally in time and under suitable assumptions on the data) an identification problem related to a linear parabolic equation when the additional information is time-dependent and nonlocal in space. More exactly, our problem consists in recovering a (positive) time-dependent coefficient β in front of the time derivative. We prove a local in time existence, uniqueness and stability result when the data belong to suitable function spaces. Our basic tool is the Semigroup Theory of linear bounded operators.
Key words.: First-order differential equations in general Banach spaces; recovering an unknown time-dependent term from which the equation depends nonlinearly; analytic semigroup theory; locally in time existence and uniqueness results; applications to identification problems for second-order parabolic linear equations
Received: 2007-10-19
Published Online: 2008-09-11
Published in Print: 2008-July
© de Gruyter 2008
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Artikel in diesem Heft
- Definitions and examples of inverse and ill-posed problems
- Recovering a scalar time dependent function in a multidimensional parabolic equation by a nonlocal boundary additional information
- A uniqueness result and image reconstruction of the orthotropic conductivity in magnetic resonance electrical impedance tomography
- Solving a scalar degenerate multidimensional identification problem in a Banach space
Schlagwörter für diesen Artikel
First-order differential equations in general Banach spaces;
recovering an unknown time-dependent term from which the equation depends nonlinearly;
analytic semigroup theory;
locally in time existence and uniqueness results;
applications to identification problems for second-order parabolic linear equations
Artikel in diesem Heft
- Definitions and examples of inverse and ill-posed problems
- Recovering a scalar time dependent function in a multidimensional parabolic equation by a nonlocal boundary additional information
- A uniqueness result and image reconstruction of the orthotropic conductivity in magnetic resonance electrical impedance tomography
- Solving a scalar degenerate multidimensional identification problem in a Banach space
