Structural Diffusion and Long-Run Growth : A Partial Differential Equation Framework

Most formal growth models describe long-run dynamics within low-dimensional aggregate state spaces, relying on ordinary differential equations (ODEs) to capture accumulation processes. While effective for medium-horizon analysis, such approaches face conceptual limitations when growth is shaped by slow structural evolution, diffusion, and persistent heterogeneity. This paper introduces a partial differential equation (PDE) framework for modeling long-run growth, treating structure as a continuous state dimension rather than a discrete regime. The framework decomposes dynamics into local accumulation, structural diffusion, and interaction effects, providing a unified formal language for representing gradual structural change and path dependence. An illustrative specification demonstrates how nonlinear diffusion–accumulation interactions can generate persistent structural gradients and heterogeneous convergence patterns, including endogenous growth slowdowns, clarifying mechanisms that remain opaque in standard aggregate models. The contribution is methodological rather than empirical. By explicitly modeling diffusion in structural space, the framework expands the analytical toolkit available for studying long-horizon economic development and structural transformation.