Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis
We consider the solvability of the semilinear parabolic differential equation \[\frac{\partial u}{\partial t}(x,t)- \Delta u(x,t) + c(x,t)u(x,t) = \mathcal{P}(u) + \gamma (x,t)\] in a cylinder \(D=\Omega \times (0,T)\), where \(\mathcal{P}\) is a hysteresis operator of Preisach type. We show that...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2008-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol28/1/art/opuscula_math_2804.pdf |
| Summary: | We consider the solvability of the semilinear parabolic differential equation \[\frac{\partial u}{\partial t}(x,t)- \Delta u(x,t) + c(x,t)u(x,t) = \mathcal{P}(u) + \gamma (x,t)\] in a cylinder \(D=\Omega \times (0,T)\), where \(\mathcal{P}\) is a hysteresis operator of Preisach type. We show that the corresponding initial boundary value problems have unique classical solutions. We further show that using this existence and uniqueness result, one can determine the properties of the Preisach operator \(\mathcal{P}\) from overdetermined boundary data. |
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| ISSN: | 1232-9274 |