Self-similar solutions of convection-diffusion processes
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TL;DRAbstract
Geometric properties of self-similar solutions to the equation $ u_t = u_{xx} + \gamma(u^q)_x,\ x > 0,\ t > 0 $ are studied, $ q $ is positive and $ \gamma\in \mathbb{R}\setminus\{0\}$. Two critical values of $ q $ (namely 1 and 2) appear the corresponding shapes are of very different nature.
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Geometric properties of self-similar solutions to the equation $ u_t = u_{xx} + \gamma(u^q)_x,\ x > 0,\ t > 0 $ are studied, $ q $ is positive and $ \gamma\in \mathbb{R}\setminus\{0\}$. Two critical values of $ q $ (namely 1 and 2) appear the corresponding shapes are of very different nature.
Keywords
DiffusionMathematicsConvectionStatistical physicsThermodynamicsPhysics
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