© 2019, Allerton Press, Inc. For a system of three equations of the second order we prove existence and uniqueness of solutions to the Cauchy problem and to problem with conditions on characteristics and a free surface. ...

We apply two methods for solving the inverse boundary-value problem (the so-called problem (A)) in the Cauchy statement for an analytic function and an unknown curve Γ. We obtain criteria for Γ to be the unit circle. We ...

We consider a mixed-type singular differential equation in a bounded spatial domain in a specific form and prove the unique solvability of the Tricomi problem for the mentioned equation. © 2011 Allerton Press, Inc.

We give a version of the Riemann method for solving the Cauchy problem for a linear equation with variable coefficients with leading partial derivative. © 2006 Springer Science+Business Media, Inc.