On the Cauchy Problem for a Degenerate Parabolic Equation | Zendy

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On the Cauchy Problem for a Degenerate Parabolic Equation

Author(s) -

Michael Winkler

Publication year - 2001

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/1038

Subject(s) - degenerate energy levels , parabolic partial differential equation , mathematics , cauchy problem , initial value problem , mathematical analysis , cauchy distribution , physics , partial differential equation , quantum mechanics

This note is concerned with the existence of a weak solution for a degenerate Cauehy problem of parabolic type in the n-dimensional space Rn. The degenerate property is in the sense that the matrix (a~ j (t, x)) involved in the differential operator is not necessarily positive definite. The essential idea is the construction of a suitable function space H and to prove the existence of a weak solution in H.

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