Characteristic problems with normal derivatives for hyperbolic systems

We consider characteristic problems with normal derivatives for a hyperbolic systemwith two independent variables. Using the Riemann method, we obtain solvability conditions for these problems accurate to several arbitrary constants. © 2013 Allerton Press, Inc

On solvability by quadratures conditions of boundary value problems for second order hyperbolic systems

© Sozontova E.A. 2016.In the present work we consider boundary value problems for second order hyperbolic system with higher partial derivatives uxy, vxy and uxx, vyy. The aim of the study is to find sufficient conditions for solvability of the considered problems by quadratures. We proposed a method for finding explicit solutions for the mentioned problems based on factorization of the equations in the original systems. As a result, in terms of the coefficients of these systems, we obtain 14 conditions for solvability by quadratures for each boundary value problem

Conditions for the solvability of a system of integral equations by quadratures

© 2015, Pleiades Publishing, Ltd. By reduction to Goursat problems, we obtain various versions of conditions ensuring that the solution of the system in question can be constructed in closed form

An addition to the cases of solvability of the Goursat problem in quadratures

© 2017, Pleiades Publishing, Ltd.Six new versions of solvability conditions for the Goursat problem in quadratures are formulated in terms of the coefficients of a linear inhomogeneous hyperbolic equation

Characteristic problems with normal derivatives for hyperbolic systems

We consider characteristic problems with normal derivatives for a hyperbolic systemwith two independent variables. Using the Riemann method, we obtain solvability conditions for these problems accurate to several arbitrary constants. © 2013 Allerton Press, Inc

On solvability by quadratures conditions of boundary value problems for second order hyperbolic systems

© Sozontova E.A. 2016.In the present work we consider boundary value problems for second order hyperbolic system with higher partial derivatives uxy, vxy and uxx, vyy. The aim of the study is to find sufficient conditions for solvability of the considered problems by quadratures. We proposed a method for finding explicit solutions for the mentioned problems based on factorization of the equations in the original systems. As a result, in terms of the coefficients of these systems, we obtain 14 conditions for solvability by quadratures for each boundary value problem

Characteristic problems with normal derivatives for hyperbolic systems

We consider characteristic problems with normal derivatives for a hyperbolic systemwith two independent variables. Using the Riemann method, we obtain solvability conditions for these problems accurate to several arbitrary constants. © 2013 Allerton Press, Inc

Characteristic problems with normal derivatives for hyperbolic systems

We consider characteristic problems with normal derivatives for a hyperbolic systemwith two independent variables. Using the Riemann method, we obtain solvability conditions for these problems accurate to several arbitrary constants. © 2013 Allerton Press, Inc

On solvability by quadratures conditions of boundary value problems for second order hyperbolic systems

© Sozontova E.A. 2016.In the present work we consider boundary value problems for second order hyperbolic system with higher partial derivatives uxy, vxy and uxx, vyy. The aim of the study is to find sufficient conditions for solvability of the considered problems by quadratures. We proposed a method for finding explicit solutions for the mentioned problems based on factorization of the equations in the original systems. As a result, in terms of the coefficients of these systems, we obtain 14 conditions for solvability by quadratures for each boundary value problem

Conditions for the solvability of a system of integral equations by quadratures

© 2015, Pleiades Publishing, Ltd. By reduction to Goursat problems, we obtain various versions of conditions ensuring that the solution of the system in question can be constructed in closed form