This article is cited in 3 papers

Solvability of nonlinear parabolic problems

M. M. Lavrent'ev (Jn.)


Abstract: We obtain estimates for gradients of solutions to some parabolic equations not satisfying the known conditions of the Bernstein type. The estimates are valid for special initial data which depend on properties of solutions to the ordinary differential equations that determine stationary solutions to parabolic equations. In consequence to the estimates obtained, we infer theorems on classical solvability of the parabolic problems under consideration.

UDC: 517.95

Received: 10.11.1992

 English version: Siberian Mathematical Journal, 1993, 34:6, 1110–1116

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