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

The uniqueness of classical solutions to inverse parabolic semilinear problems together with nonlocal initial conditions with integrals, for the operator ∑i,j=1n∂∂xi(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,..., x_n), 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.