On the existence of solutions of one nonlinear boundary-value problem for shallow shells of Timoshenko type with simply supported edges

11th International Conference on "Mesh methods for boundary-value problems and applications"

Timergaliev, S.N.^1 ; Kharasova, L.S.^2

Department of Higher Mathematics KGASU, Republic of Tatarstan, Zelenaya street, 1, Kazan

420043, Russia^1

Department of Mathematics Naber, Ezhnye Chelny Institute, Kazan Federal University, Republic of Tatarstan, Naberezhnye Chelny, 68/19, 423812, Russia^2

关键词: Cauchy-Riemann equations;    Existence of Solutions;    Initial conditions;    Integral representation;    Nonlinear boundary value problems;    Nonlinear operator equations;    Second-order partial differential equation;    System of equations;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/158/1/012092/pdf
DOI  :  10.1088/1757-899X/158/1/012092

来源: IOP

【 摘 要 】

Solvability of one system of nonlinear second order partial differential equations with given initial conditions is considered in an arbitrary field. Reduction of the initial system of equations to one nonlinear operator equation is used to study the problem. The solvability is established with the use of the principle of contracting mappings. The method used in these studies is based on the integral representations for the displacements. These representations are constructed with the use of general solutions to the inhomogeneous Cauchy-Riemann equation.