Integral transforms and factorization method for boundary problems. (Russian) Zbl 1082.35010

The double factorization method is developed for systems of partial differential equations with permanent coefficients of an arbitrary finite order over a bounded simply-connected convex domain \(\Omega\) with boundary \(\partial \Omega\). By virtue of earlier published transforms, an initial system is reduced to the expression \[ \mathbf K\phi = -{\mathbf G}(\alpha) + \iint_{\partial \Omega}\omega. \] Having applied the double factorization method, the solution to the boundary problem is constructed.


35A22 Transform methods (e.g., integral transforms) applied to PDEs
35E20 General theory of PDEs and systems of PDEs with constant coefficients
35G30 Boundary value problems for nonlinear higher-order PDEs