Investigation of the extended fisher-kolmogorov equation shows global existence and uniqueness in three dimensions, indicating strong and weak solutions.
We investigate the extended Fisher-Kolmogorov equation (EFK) under Neumann boundary conditions in a spatial dimension of up to three (d≤ 3). This is done on a bounded convex domain with a boundary that possesses C² smoothness. The EFK equation, which is a fourth-order PDE, is reduced into a system of two second-order PDEs. We prove the global existence, uniqueness, and continuous dependence on initial conditions for both strong and weak solutions using Lions' classic Faedo-Galerkin approach and compactness arguments. Furthermore, we provide results on the regularity of weak forms.
No takes yet. Share an insight, caveat, or question.
Al-Musawi et al. (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: