Vol. 46, No. 1, 1973

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Uniqueness for the Cauchy problem for degenerate parabolic equations

Avner Friedman

Vol. 46 (1973), No. 1, 131–147

Consider a second order degenerate parabolic operator L. The present paper is concerned with the uniqueness of solutions of the Cauchy problem: Lu = f in a strip 0 < t T, u(0,x) = ϕ(x) for all x in Rn. It is proved that there is at most one solution subject to a growth condition which depends on the degeneracy of L. In the special case where L is ultraparabolic, uniqueness is proved under only onesided growth condition. The methods used involve the construction of comparison functions in suitable sequences of domains.

Mathematical Subject Classification 2000
Primary: 35K15
Received: 18 February 1972
Published: 1 May 1973
Avner Friedman