Initial-Mixed Boundary Value Problems for Nonlinear Parabolic Complex Equations of Second Order with Measurable Coefficients

Abstract:: This paper deals with the initial-mixed boundary value problem for nonlinear parabolic equations of second order with measurable coefficients in a multiply connected domain. Firstly, we give a priori estimates of solutions for the above initial- boundary value problem with some conditions, afterwards by using the above estimates of solutions and the compactness principle of solutions, the existence of solutions for the above problem is proved. Here the condition (1.4) is weaker than the corresponding condition in [1] and [4], i.e. the constant 4/3 in [1] and [4] is replaced by 3/2 in (1.4).
Key wards:: initial-mixed problems; parabolic equations; measura- ble coefficients

(R.D. 1995-03-14 P.D. 1995-09-20 Vol.31 No.5 pp.511-519)

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