Communications in Mathematical Sciences

Volume 1 (2003)

Number 4

Uniqeness of BV Entropy Solutions for High Dimensional Quasilinear Parabolic Equations with Arbitrary Degeneracy

Pages: 697 – 714



Yin Jingxe

Lei Peidong

Wu Zhuoqun


This paper deals with the Cauchy problem for the quasilinear parabolic equations with arbitrary degeneracy. We give a new and natural definition of BV entropy solution. The uniqueness of the natural BV entropy solutions is obtained. In order to prove the uniqueness, the discontinuity conditions for these solutions are established. Also, we construct an example of the natural BVentropy solution.

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