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DTIC ADA120447: A Nonlinear Functional Differential Equation in Ban... |
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by Defense Technical Information Center |
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The report studies a nonlinear functional differential |
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equation in Banach space. This equation is an abstract |
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form of the equations of motion for nonlinear materials |
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with fading memory. Its basic structure is hyperbolic in |
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character so that global smooth solutions should not be |
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expected in general. Memory effects, however, may induce |
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a dissipative mechanism which, although very subtle, is |
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effective so long as the solution is small. The report |
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shows that if the memory is dissipative in an appropriate |
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sense, then the history value problem associated with our |
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equation has a unique global smooth solution provided the |
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initial history and forcing are suitably smooth and |
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small. The proof combines a fixed point argument to |
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establish local existence with a chain of global a priori |
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'energy-type' estimates. The abstract results are then |
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applied to establish global existence of smooth solutions |
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to certain history value problems associated with the |
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motion of nonlinear materials with fading memory, under |
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assumptions which are realistic within the framework of |
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continuum mechanics. |
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Date Published: 2018-01-07 09:42:17 |
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Identifier: DTIC_ADA120447 |
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Item Size: 32714587 |
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Language: english |
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Media Type: texts |
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# Topics |
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DTIC Archive; Hrusa,William J ; ACURE... |
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# Collections |
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dticarchive |
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additional_collections |
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# Uploaded by |
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@chris85 |
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