ON POTENTIALIZED PARTIAL-DIFFERENTIAL EQUATIONS IN THEORETICAL SPATIAL ECONOMICS

For use in theoretical spatial economics, classical partial differenti al equations should be generalized by potentializing the spatial varia bles; this has been undertaken for the one-dimensional wave equation. Three potentials (linear, exponential, Tanner) have been investigated; the exponential one especially has led to meaningful analytical solut ions in terms of spatial economic patterns. Problems of stability and 'strangeness' of the dynamical solutions are discussed, and lines for further research set out.