Inverse boundary value problem for a Boussinesq type nonlinear differential equation
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This article considers the questions of one value solvability of the inverse boundary value problem for a nonlinear Boussinesq type fourth-order integro-differential equation. The Fourier method of separation of variables is employed and is obtained the countable system of nonlinear integral equations (CSNIE). To prove the theorem of one value solvability of CSNIE is used the method of successive approximations. Further the article shows the convergence of the obtained Fourier series to the unknown function of boundary value problem and the stability of solution of the considering integro-differential equation with respect to restore Function. This paper advances the theory of partial differential equations with weak nonlinear hand-side.
Abstract
This article considers the questions of one value solvability of the inverse boundary value problem for a nonlinear Boussinesq type fourth-order integro-differential equation. The Fourier method of separation of variables is employed and is obtained the countable system of nonlinear integral equations (CSNIE). To prove the theorem of one value solvability of CSNIE is used the method of successive approximations. Further the article shows the convergence of the obtained Fourier series to the unknown function of boundary value problem and the stability of solution of the considering integro-differential equation with respect to restore Function. This paper advances the theory of partial differential equations with weak nonlinear hand-side.
참고문헌 (12)
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