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End effects in the dynamical problem of magneto-elasticity. (English) Zbl 1038.74019

Summary: We derive spatial decay bounds for the solutions of linear dynamical problem of magneto-elasticity in a semi-infinite cylindrical region. For the forward-in-time problem we prove that an energy expression is bounded from above by a decaying exponential of a quadratic polynomial of the distance. We derive a spatial decay estimate for backward-in-time problem as well. The proof works only if the cross-section is a finite union of rectangles with axes parallels to \(0x_2\) and \(0x_3\). As a conclusion, we extend the above bound to the heat conduction case.

MSC:

74F15 Electromagnetic effects in solid mechanics
74F05 Thermal effects in solid mechanics
35Q72 Other PDE from mechanics (MSC2000)
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