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Determining of three unknown functions of a semilinear ultraparabolic equation
Authors:Nataliya Protsakh
Abstract:In this paper, we consider the inverse problem for second‐order semilinear ultraparabolic equation. The equation has unknown function of time variable in its minor coefficient and two unknown functions of time and spacial variables in its right‐hand side. Initial, boundary, and integral type overdetermination conditions are posed. By using the properties of the solutions of the corresponding initial‐boundary value problem and the method of successive approximations, the sufficient conditions of the existence, and the uniqueness of the solution for the inverse problem are obtained on some time interval that depends on the coefficients of the equation.
Keywords:existence of solution  initial‐boundary value problem  inverse problem  successive approximations method  ultraparabolic equation  uniqueness of solution
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