A Nonlinear Parabolic - Sobolev Equation
نویسنده
چکیده
Let M and I, be (nonlinear) operators in a reflexive Banach space B for which Rg(M + L) = B and j(Mx My) i~(Lx Ly)( > / Mx My / for all 01 > 0 and pairs s, y in D(M) n D(L). Then there is a unique solution of the Cauchy problem (Mu(t))’ + Lu(t) = 0, Mu(O) = v0 . When M and L are realizations of elliptic partial differential operators in space variables, this gives existence and uniqueness of generalized solutions of boundary value problems for nonlinear partial differential equations of mixed parabolicSobolev type.
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تاریخ انتشار 2003