Prolongation of classical solutions and singularities of generalized solutions

Fundamental Solutions of Dynamic Poroelasticity and Generalized Termoelasticity

Fundamental solutions of dynamic poroelasticity and generalized thermoelasticity are derived in the Laplace transform domain. For poroelasticity, these solutions define the solid displacement field and the fluid pressure in fluid-saturated media due to a point force in the solid and an injection of fluid in the pores. In addition, approximate fundamental solutions for short times are derived by...

Quantum corrections to classical solutions via generalized zeta-function

A general algebraic method of quantum corrections evaluations is presented. Quantum corrections to a few classical solutions of Landau-Ginzburg model (phi-in-quadro) are calculated in arbitrary dimensions. The Green function for heat equation with soliton potential is constructed by Darboux transformation. The generalized zeta-function is used to evaluate the functional integral and corrections...

Exact Solutions of the Generalized Kuramoto-Sivashinsky Equation

In this paper we obtain  exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    The methods used  to determine the exact solutions of the underlying equation are the Lie group analysis  and the simplest equation method. The solutions obtained are  then plotted.

Singular Solutions and Prolongation of Holomorphic Solutions to Nonlinear Differential Equations

Costing Non-classical Solutions to the Paradoxes of Self-reference 1 Non-classical Solutions

The paradoxes of self-reference are genuinely paradoxical. The liar paradox, Russell's paradox and their cousins pose enormous diiculties to anyone who seeks to give a comprehensive theory of semantics, or of sets, or of any other domain which allows a modicum of self-reference and a modest number of logical principles. One approach to the paradoxes of self-reference takes these paradoxes as mo...