Symmetry Breaking and Exact Solutions of the Hyperbolic Heat Equation with Variable Medium Properties
نویسنده
چکیده
We classify from Lie symmetry standpoint the hyperbolic heat equation with temperature-dependent medium properties. We prove that the hyperbolic heat equation may admit a two-, three-, fouror infinitedimensional symmetry Lie algebra depending on the functional form of density, thermal conductivity, and specific heat. The last possibility corresponds to exactly linearizable hyperbolic heat equation. The symmetry structure of the hyperbolic heat equation is used to optimally classify similarity solutions. Also we employ group foliation technique to obtain separable solutions of the hyperbolic heat equation. Mathematics Subject Classification: 76M60, 76G65, 81R40
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