## Abstract

In this paper we have proved that the Dirichlet problem for the forward-backward p-parabolic equation has an entropy measurevalued solution which has been obtained as a singular limit of weak solutions and their gradients to the Dirichlet problem for the elliptic equation containing the anisotropic (p, 2)-Laplace operator. In order to guarantee the existence of entropy measure-valued solutions, the initial and final conditions should be formulated in the form of integral inequalities. This means that an entropy measure-valued solution can deviate from both initial and final data on the boundary. Moreover, a gradient Young measure appears in the representation of an entropy measurevalued solution. The uniqueness of entropy measure-valued solutions is still an open question.

Original language | English |
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Pages (from-to) | 774-793 |

Number of pages | 20 |

Journal | Сибирские электронные математические известия |

Volume | 14 |

DOIs | |

Publication status | Published - 1 Jan 2017 |

## Keywords

- Anisotropic Laplace operator
- Entropy measure-valued solution
- Forward-backward parabolic equation
- Gradient Young measure

## OECD FOS+WOS

- 1.01 MATHEMATICS