Mathematical analysis of extended Fisher-Kolmogorov equation with Neumann boundary conditions

Ghufran  A. Al-Musawi; Akil Harfash

doi:10.5269/bspm.69863

Ghufran A. Al-Musawi Department of Mathematics, College of Sciences, University of Basrah
Akil Harfash University of Basrah

Resumo

We investigate the extended Fisher-Kolmogorov equation (EFK) under Neumann boundary conditions in a spatial dimension of up to three ($d\leq 3$). This is done on a bounded convex domain with a boundary that possesses $C^{2}$ 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.

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