Abstract:
In this paper, we consider a quasilinear parabolic equation in nontube domain, which degenerate on a solution. We suppose the essential boundedness of the derivative of the function that define the curvilinear boundary, and prove an existence and uniqness theorems for the first boundary-value problem. We use compactness methods for functions from Banach space scale. At the Preliminary part establish abstract theorems about completeness certain system of function in nontube domain.
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