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Modeling of physical phenomena almost always relies on some kind of conservation, such as conservation of energy, mass, momentum. In this final project, we discuss a class of systems of partial differential equation to describe conservation phenomena, which is called Conservation Laws. Conservation...
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id-itb.:73212017-09-27T11:43:03Z#TITLE_ALTERNATIVE# LAILATUL LATIFAH (NIM 10104088), ARNIDA Indonesia Final Project INSTITUT TEKNOLOGI BANDUNG https://digilib.itb.ac.id/gdl/view/7321 Modeling of physical phenomena almost always relies on some kind of conservation, such as conservation of energy, mass, momentum. In this final project, we discuss a class of systems of partial differential equation to describe conservation phenomena, which is called Conservation Laws. Conservation laws may not admit solutions in regular sense; the notion of solutions need to be relaxed to admit discontinuous ones. As the notion of solution becomes weaker, uniqueness is lost; therefore additional condition must be assumed to have uniqueness back. This condition is called entropy. Propagation of discontinuities is studied through Rankine-Hugoniot condition, both for scalar equations, and for systems, in particular in the cases of linear and quasi linear hyperbolic. In all the cases, finite speed of propagation, which is a hallmark of wave equation, exhibited; and thus establishes the fact that conservation laws is really a class of wave equations. text |
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Modeling of physical phenomena almost always relies on some kind of conservation, such as conservation of energy, mass, momentum. In this final project, we discuss a class of systems of partial differential equation to describe conservation phenomena, which is called Conservation Laws. Conservation laws may not admit solutions in regular sense; the notion of solutions need to be relaxed to admit discontinuous ones. As the notion of solution becomes weaker, uniqueness is lost; therefore additional condition must be assumed to have uniqueness back. This condition is called entropy. Propagation of discontinuities is studied through Rankine-Hugoniot condition, both for scalar equations, and for systems, in particular in the cases of linear and quasi linear hyperbolic. In all the cases, finite speed of propagation, which is a hallmark of wave equation, exhibited; and thus establishes the fact that conservation laws is really a class of wave equations. |
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Final Project |
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LAILATUL LATIFAH (NIM 10104088), ARNIDA |
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LAILATUL LATIFAH (NIM 10104088), ARNIDA #TITLE_ALTERNATIVE# |
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LAILATUL LATIFAH (NIM 10104088), ARNIDA |
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LAILATUL LATIFAH (NIM 10104088), ARNIDA |
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https://digilib.itb.ac.id/gdl/view/7321 |
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