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Uniqueness theorems for a nonlinear Tricomi problem and the related evolution problem
Author(s) -
Lar'kin N. A.,
Schneider M.
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670180802
Subject(s) - mathematics , uniqueness , boundary value problem , operator (biology) , mathematical analysis , initial value problem , nonlinear system , partial differential equation , biochemistry , chemistry , physics , repressor , quantum mechanics , transcription factor , gene
We consider an initial‐boundary value problem for the non‐linear evolution equationin a cylinder Q t = Ω × (0, t ), where T [ u ] = yu xx + u yy is the Tricomi operator and l ( u ) a special differential operator of first order. In [10] we proved the existence of a generalized solution of problem (1) and the existence of a generalized solution of the corresponding stationary boundary value problem (non‐linear Tricomi problem)In this paper we give sufficient conditions for the uniqueness of these solutions.