Page 219 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 219
TOPOLOGICAL METHODS IN DIFFERENTIAL EQUATIONS (MS-13)
On the stability of the oscillations for some singular models
Jose Angel Cid, angelcid@uvigo.es
University of Vigo, Spain
We present some sufficient conditions for the existence and Lyapunov stability of periodic so-
lutions for a kind of equations allowing singularities. Our approach relies on the third order
approximation and the averaging method. We will provide applications to some singular mod-
els like the Brillouin beam focusing equation.
The talk is based on the paper Wang, F., Cid, J. Á., Li, S. and Zima, M., Lyapunov stability
of periodic solutions of Brillouin type equations, Appl. Math. Lett. 101 (2020).
Multiple oscillating BV-solutions for a mean-curvature Neumann problem
Francesca Colasuonno, francesca.colasuonno@unibo.it
Università di Bologna, Italy
Coauthors: Alberto Boscaggin, Colette De Coster
In this talk, I will focus on a one-dimensional mean-curvature problem under Neumann bound-
ary conditions. I will describe how we can find multiple positive oscillating BV-solutions, using
an approximation of the mean curvature operator and the shooting method. This is joint work
with Alberto Boscaggin and Colette De Coster.
Traveling waves for advection-reaction-diffusion equations with negative
diffusivity
Andrea Corli, crl@unife.it
University of Ferrara, Italy
Coauthors: Diego Berti, Luisa Malaguti
In the talk I shall present some recent results, motivated by the modeling of collective move-
ments, about traveling-wave solutions for advection-reaction-diffusion equations
ut + f (u)x = (D(u)ux)x + g(u),
with g(0) = g(1) = 0 and u ∈ [0, 1]. The main issue is that the diffusivity D, that may vanish
at 0 or 1, can be negative. More precisely, we first deal with the case when g > 0 in (0, 1) and
D changes sign once, either from the positive to the negative or conversely. These results are
extended to a finite number of sign changes of D. Then, we also admit the source term g to
change sign.
In every case, the presence of the convective term f leads to new behaviors of the profiles
with respect to the pure reaction-diffusion case.
References
[1] D. Berti, A. Corli, L. Malaguti. Uniqueness and nonuniqueness of fronts for degenerate
diffusion-convection reaction equations. Electron. J. Qual. Theory Differ. Equ., Paper No.
66, 34 pages, 2020.
217
On the stability of the oscillations for some singular models
Jose Angel Cid, angelcid@uvigo.es
University of Vigo, Spain
We present some sufficient conditions for the existence and Lyapunov stability of periodic so-
lutions for a kind of equations allowing singularities. Our approach relies on the third order
approximation and the averaging method. We will provide applications to some singular mod-
els like the Brillouin beam focusing equation.
The talk is based on the paper Wang, F., Cid, J. Á., Li, S. and Zima, M., Lyapunov stability
of periodic solutions of Brillouin type equations, Appl. Math. Lett. 101 (2020).
Multiple oscillating BV-solutions for a mean-curvature Neumann problem
Francesca Colasuonno, francesca.colasuonno@unibo.it
Università di Bologna, Italy
Coauthors: Alberto Boscaggin, Colette De Coster
In this talk, I will focus on a one-dimensional mean-curvature problem under Neumann bound-
ary conditions. I will describe how we can find multiple positive oscillating BV-solutions, using
an approximation of the mean curvature operator and the shooting method. This is joint work
with Alberto Boscaggin and Colette De Coster.
Traveling waves for advection-reaction-diffusion equations with negative
diffusivity
Andrea Corli, crl@unife.it
University of Ferrara, Italy
Coauthors: Diego Berti, Luisa Malaguti
In the talk I shall present some recent results, motivated by the modeling of collective move-
ments, about traveling-wave solutions for advection-reaction-diffusion equations
ut + f (u)x = (D(u)ux)x + g(u),
with g(0) = g(1) = 0 and u ∈ [0, 1]. The main issue is that the diffusivity D, that may vanish
at 0 or 1, can be negative. More precisely, we first deal with the case when g > 0 in (0, 1) and
D changes sign once, either from the positive to the negative or conversely. These results are
extended to a finite number of sign changes of D. Then, we also admit the source term g to
change sign.
In every case, the presence of the convective term f leads to new behaviors of the profiles
with respect to the pure reaction-diffusion case.
References
[1] D. Berti, A. Corli, L. Malaguti. Uniqueness and nonuniqueness of fronts for degenerate
diffusion-convection reaction equations. Electron. J. Qual. Theory Differ. Equ., Paper No.
66, 34 pages, 2020.
217
