Akhundov A. Ya.
Determination of the Coefficient of a Semilinear Parabolic Equation for a Boundary-Value Problem with Nonlinear Boundary Condition
Ukr. Mat. Zh. - 2014. - 66, № 6. - pp. 847–852
We study the well-posedness of the inverse problem of determination of the coefficient of a minor term of a semilinear parabolic equation in the presence of a nonlinear boundary condition. The additional condition is given in the nonlocal integral form. A uniqueness theorem and a “conditional” stability theorem are proved.
Ukr. Mat. Zh. - 2006. - 58, № 1. - pp. 115–124
The questions of well-posedness and approximate solution of inverse problems of finding unknown functions on the right-hand side of a system of parabolic equations are investigated. For the problems considered, theorems on the existence, uniqueness, and stability of a solution are proved and examples that show the exactness of the established theorems are given. Moreover, on the set of well-posedness, the rate of convergence of the method of successive approximations suggested for the approximate solution of the given problems is estimated.