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Vectorial quasilinear diffusion equation with dynamic boundary condition

Nakayashiki, Ryota (2017)

Proceedings of Equadiff 14

In this paper, we consider a class of initial-boundary value problems for quasilinear PDEs, subject to the dynamic boundary conditions. Each initial-boundary problem is denoted by (S) ε with a nonnegative constant ε , and for any ε ≥ 0 , (S) ε can be regarded as a vectorial transmission system between the quasilinear equation in the spatial domain Ω , and the parabolic equation on the boundary Γ : = ∂ Ω , having a sufficient smoothness. The objective of this study is to establish a mathematical method, which can...

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