TY  - JOUR
ID  - Jais2008
LB  - Jais2008
AU  - Jais, Mathias
TI  - Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis
ST  - Classical and weak solutions for semilinear parabolic equations with Preisach hysteresis
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2008
VL  - 28
IS  - 1
SP  - 47
EP  - 62
DO  - http://dx.doi.org/10.7494/OpMath.2008.28.1.47
UR  - http://dx.doi.org/10.7494/OpMath.2008.28.1.47
AB  - 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.
KW  - hysteresis
KW  - parabolic
KW  - inverse problem
KW  - uniqueness
SN  - 1232-9274
ER  -