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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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 |
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doaj-51fef271432f4442ba043f546fcb11332020-11-25T00:32:53ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742008-01-0128147622804Classical and weak solutions for semilinear parabolic equations with Preisach hysteresisMathias Jais0Cardiff University, School of Computer Science, Cardiff, CF24 3AA, U.K.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.http://www.opuscula.agh.edu.pl/vol28/1/art/opuscula_math_2804.pdfhysteresisparabolicinverse problemuniqueness |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Mathias Jais |
| spellingShingle |
Mathias Jais Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis Opuscula Mathematica hysteresis parabolic inverse problem uniqueness |
| author_facet |
Mathias Jais |
| author_sort |
Mathias Jais |
| title |
Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis |
| title_short |
Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis |
| title_full |
Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis |
| title_fullStr |
Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis |
| title_full_unstemmed |
Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis |
| title_sort |
classical and weak solutions for semilinear parabolic equations with preisach hysteresis |
| publisher |
AGH Univeristy of Science and Technology Press |
| series |
Opuscula Mathematica |
| issn |
1232-9274 |
| publishDate |
2008-01-01 |
| description |
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. |
| topic |
hysteresis parabolic inverse problem uniqueness |
| url |
http://www.opuscula.agh.edu.pl/vol28/1/art/opuscula_math_2804.pdf |
| work_keys_str_mv |
AT mathiasjais classicalandweaksolutionsforsemilinearparabolicequationswithpreisachhysteresis |
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1725318561658830848 |