Finding the coefficient multiplying the time derivative in quasilinear parabolic equations in Hölder spaces
N. L. Gol’dman · Differential Equations · 2012
We justify statements in Hölder classes of ill-posed inverse problems with terminal observation for parabolic equations with unknown coefficients multiplying the time derivative. On the basis of the duality principle, we prove sufficient conditions for the uniqueness of solutions in these classes. We present examples in which the uniqueness property is lost if the set of admissible solutions is extended and examples of instability of the solutions with respect to errors in the input data. We justify the quasisolution method for constructing approximate solutions stable in these Hölder classes.