Singular solutions of the related equation systems will be derived for situations involving components with very low or null transmissivity.
These functions are derived from the singular solutions of the Laplace problem.
It is based on a splitting of the space of solutions in a regular subspace, and a singular one, derived from the singular solutions of the Laplace problem.
For second- and higher-order strongly nonlinear differential equations, Kiguradze proved the existence of singular solutions of the first and the second kind and proper solutions of various types (bounded, vanishing at infinity, slowly increasing, rapidly increasing, etc).
We deal with the self-similar singular solution of doubly singular parabolic equation with a gradient absorption term for, and in.
The non-singular solutions of the linearized perturbation equation given by the systems (21 - 25 21 - 25e solutions (16)-(17) of the unperturbed systems (12)-(14) must sandsfy certhen boundary conditionsolutions
The non-singular solutions of the linearized perturbation equations give ϕ,V, and ψ as follows: ϕ 1 ( i ) = A 1 t I m k r exp i k z + m φ, (21) V 1 ( i ) = B 1 t I m k r exp i k z + m φ, (22) V 1 ( e ) = B 2 t K m k r exp i k z + m φ (23) ψ 1 ( i ) = C 1 t I m k r exp i k z + m φ (24) ψ 1 ( e ) = C 2 t K m k r exp i k z + m φ, (25).
In this paper the singular solutions of linear elastostatics are derived, and two new models of interior crack singularity are proposed.
In this paper, in order to develop a method which overcomes this difficulty, the singular solutions of isotropic and anisotropic Helmholtz-type equations with homogeneous Dirichlet and/or Neumann boundary conditions in the neighbourhood of a singular point are derived.
