On stability of a stationary solution to the Hotelling migration equation

On the Stability of Stationary States in Diffusion Models in Biology and Humanities

“…However, in the case B = 0, as already noted, the trivial solution is unstable, and in the case B > 0 the trivial solution is stable. Below we extend the results of [16,17] to one class of systems of partial differential equations.…”

“…Let w = (w 1 , w 2 ) be a stationary solution of the problem ( 17)- (19). Coefficients (15) of a quadratic form (14) for system (17) have the form…”

“…In the monograph by T. Puu [13], using the Lyapunov function (Alexander Mikhailovich Lyapunov, 1857-1918) of a special kind, a sufficient condition for the stability of a regular stationary solution w of the initial boundary value problem with a boundary condition of the first, second or third kind for the Hotelling equation ( 2) in a bounded domain was found in the form w > ξ/2. Later this condition was improved (weakened), namely, it was shown that the condition w > ξ/2 − B/ 2Ad 2 is sufficient for the stability of a stationary solution w(x, y) of the initial boundary value problem with a boundary condition of condition of the first, second or third kind for the Hotelling equation ( 2) in a bounded domain with a diameter of d (see [16,17]). This condition for B > 0 is satisfied for a small diameter of the domain Ω.…”

On the stability of stationary solutions in diffusion models of oncological processes

“…In the paper [46], the methods of the work [40] were applied to a more complex equation, also considered in [45].…”

Stability of stationary solutions for the glioma growth equations with radial or axial symmetries

“…The above result was developed by Gogoleva et al, 35 and following the arguments of Puu, 33 they considered the equation where are two constant vectors, determining the intensity and direction of autonomous components movements. All variables are dimensionless.…”