| Abstract: |
| We consider one-dimensional Cauchy problems (CP) for scalar parabolic-hyperbolic conservation laws. The equation is regarded as a linear combination of the scalar hyperbolic conservation laws and the porous medium type equations. Thus, this equation has both properties of hyperbolic equations and those of parabolic equations. Accordingly, it is difficult to investigate the behavior of solutions to (CP).
In this talk, we construct shock waves and discuss the properties of them. Moreover, we explain the properties of rarefaction waves using super-solutions and sub-solutions. |
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