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Keywords:
quasilinear; method of Minty-Browder type; existence; uniqueness; weak $\omega$-periodic solution; vibrating processes; elasto-plastic solids; ferromagnetics; Ishlinskii hysteresis operator; finite speed of propagation; sharp estimates; hysteresis energy losses
quasilinear; method of Minty-Browder type; existence; uniqueness; weak $\omega$-periodic solution; vibrating processes; elasto-plastic solids; ferromagnetics; Ishlinskii hysteresis operator; finite speed of propagation; sharp estimates; hysteresis energy losses
Summary:
A version of the Minty-Browder method is used for proving the existence and uniqueness of a weak $\omega$-periodic solution to the equation $u_{tt}\rightarrow \text {div} F(\text {grad } u)= g$ in a bounded domain $\Omega \subset \bold R^N$ with the boundary condition $u=0$ on $\delta \Omega$, where $g$ is a given (generalized) $\omega$-periodic function and $F$ is the Ishlinskii hysteresis operator.
References:
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