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Uniqueness of Solutions to Inverse Parabolic Semilinear Problems under Nonlocal Conditions with Integrals


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The uniqueness of classical solutions to inverse parabolic semilinear problems together with nonlocal initial conditions with integrals, for the operator i,j=1nxi(aij(x,t)xj)+v(x,t)-t,\sum\limits_{i,j = 1}^n {{\partial \over {\partial {x_i}}}\left( {{a_{ij}}\left( {x,t} \right){\partial \over {\partial {x_j}}}} \right)} + v\left( {x,t} \right) - {\partial \over {\partial t}},, x=(x1,..., xn), in the cylindrical domain D:= D0×(t0, t0+T) ⊂ℜn+1, where t0∈ℜ, 0 < T <∞ are studied. The result consists in the introduction of nonlocal conditions with integrals.

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