Radial symmetric stationary solutions for a MEMS type reaction–diffusion equation with spatially dependent nonlinearity.

Autor: Ichida, Yu, Sakamoto, Takashi Okuda
Zdroj: Japan Journal of Industrial & Applied Mathematics; 2021, Vol. 38 Issue 1, p297-322, 26p
Abstrakt: We consider the radial symmetric stationary solutions of u t = Δ u - | x | q u - p . We first give a result on the existence of the negative value functions that satisfy the radial symmetric stationary problem on a finite interval for p ∈ 2 N , q ∈ R . Moreover, we give the asymptotic behavior of u(r) and u ′ (r) at both ends of the finite interval. Second, we obtain the existence of the positive radial symmetric stationary solutions with the singularity at r = 0 for p ∈ N and q ≥ - 2 . In fact, the behavior of solutions for q > - 2 and q = - 2 are different. In each case of q = - 2 and q > - 2 , we derive the asymptotic behavior for r → 0 and r → ∞ . These facts are studied by applying the Poincaré compactification and basic theory of dynamical systems. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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