Geodesic
A monotonicity method for solving hyperbolic problems with hysteresis
Applications of Mathematics, Tome 33 (1988) no. 3, pp. 197-203.

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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.
DOI : 10.21136/AM.1988.104302
Classification : 35B10, 35B40, 35L70, 74H45, 74H99
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 
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     author = {Krej\v{c}{\'\i}, Pavel},
     title = {A monotonicity method for solving hyperbolic problems with hysteresis},
     journal = {Applications of Mathematics},
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     url = {http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104302/}
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Krejčí, Pavel. A monotonicity method for solving hyperbolic problems with hysteresis. Applications of Mathematics, Tome 33 (1988) no. 3, pp. 197-203. doi : 10.21136/AM.1988.104302. http://geodesic.mathdoc.fr/articles/10.21136/AM.1988.104302/

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