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| Strongly degenerate parabolic equations are regarded as a linear combination of the time-dependent conservation laws (quasilinear hyperbolic equations) and the porous medium type equations (nonlinear degenerate parabolic equations). Thus, these equations have both properties of hyperbolic equations and those of parabolic equations and describe various nonlinear convective diffusion phenomena such as filtration problems, Stefan problems and so on.
In this talk we consider strongly degenerate parabolic equations with diffusion coefficients depending on the spatial variable. In particular, we formulate entropy solutions associated with the equations and prove the existence and uniqueness of its. |
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