Uniqueness theorems for a nonlinear Tricomi problem and the related evolution problem

Autor:	Michael Schneider, N. A. Lar'kin
Rok vydání:	1995
Předmět:	Combinatorics Uniqueness theorem for Poisson's equation General Mathematics Operator (physics) Weak solution Mathematical analysis General Engineering Existence theorem Initial value problem Uniqueness Boundary value problem Differential operator Mathematics
Zdroj:	Mathematical Methods in the Applied Sciences. 18:591-601
ISSN:	1099-1476 0170-4214
DOI:	10.1002/mma.1670180802
Popis:	We consider an initial-boundary value problem for the non-linear evolution equation L E [u] = T[u] + R(x,y,t)uu Q + ∂/∂ t l(u) = F(x,y,t,u) ∂t in a cylinder Q f = Ω X (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) L T [u] = T[u] + r(x,y)uu Q =f(x,y,u) in Ω. (2) In this paper we give sufficient conditions for the uniqueness of these solutions.
Databáze:	OpenAIRE
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