### Abstract

We study the simplest maximal positive boundary value problem for symmetric positive systems in a bounded open set for which the boundary matrix is not of constant rank. To be precise, the boundary matrix changes the definiteness simply crossing an embedded manifold in the boundary which is the intersection of the boundary with a non-characteristic hypersurface. Assuming that the flow passing the hypersurface compensates for the degeneracy of the boundary matrix on the embedded manifold, we discuss the existence of regular solutions to the boundary value problem.

Original language | English |
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Pages (from-to) | 167-182 |

Number of pages | 16 |

Journal | Hokkaido Mathematical Journal |

Volume | 25 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1996 Jan 1 |

Externally published | Yes |

### Fingerprint

### Keywords

- Characteristic boundary
- Maximal positive boundary condition
- Not of constant rank
- Symmetric positive boundary value problem

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Hokkaido Mathematical Journal*,

*25*(1), 167-182. https://doi.org/10.14492/hokmj/1351516716

**A characteristic initial boundary value problem for a symmetric positive system.** / Nishitani, Tatsuo; Takayama, Masahiro.

Research output: Contribution to journal › Article

*Hokkaido Mathematical Journal*, vol. 25, no. 1, pp. 167-182. https://doi.org/10.14492/hokmj/1351516716

}

TY - JOUR

T1 - A characteristic initial boundary value problem for a symmetric positive system

AU - Nishitani, Tatsuo

AU - Takayama, Masahiro

PY - 1996/1/1

Y1 - 1996/1/1

N2 - We study the simplest maximal positive boundary value problem for symmetric positive systems in a bounded open set for which the boundary matrix is not of constant rank. To be precise, the boundary matrix changes the definiteness simply crossing an embedded manifold in the boundary which is the intersection of the boundary with a non-characteristic hypersurface. Assuming that the flow passing the hypersurface compensates for the degeneracy of the boundary matrix on the embedded manifold, we discuss the existence of regular solutions to the boundary value problem.

AB - We study the simplest maximal positive boundary value problem for symmetric positive systems in a bounded open set for which the boundary matrix is not of constant rank. To be precise, the boundary matrix changes the definiteness simply crossing an embedded manifold in the boundary which is the intersection of the boundary with a non-characteristic hypersurface. Assuming that the flow passing the hypersurface compensates for the degeneracy of the boundary matrix on the embedded manifold, we discuss the existence of regular solutions to the boundary value problem.

KW - Characteristic boundary

KW - Maximal positive boundary condition

KW - Not of constant rank

KW - Symmetric positive boundary value problem

UR - http://www.scopus.com/inward/record.url?scp=0002196873&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0002196873&partnerID=8YFLogxK

U2 - 10.14492/hokmj/1351516716

DO - 10.14492/hokmj/1351516716

M3 - Article

AN - SCOPUS:0002196873

VL - 25

SP - 167

EP - 182

JO - Hokkaido Mathematical Journal

JF - Hokkaido Mathematical Journal

SN - 0385-4035

IS - 1

ER -