Characteristic phenomena in combustion.
Computation of bifurcated branches in a free boundary problem arising in combustion theory
Computation of bifurcated branches in a free boundary problem arising in combustion theory
We consider a parabolic 2D Free Boundary Problem, with jump conditions at the interface. Its planar travelling-wave solutions are orbitally stable provided the bifurcation parameter does not exceed a critical value . The latter is the limit of a decreasing sequence of bifurcation points. The paper deals with the study of the 2D bifurcated branches from the planar branch, for small k. Our technique is based on the elimination of the unknown front, turning the problem into a fully nonlinear...
Computing the differential of an unfolded contact diffeomorphism
Consider a bifurcation problem, namely, its bifurcation equation. There is a diffeomorphism linking the actual solution set with an unfolded normal form of the bifurcation equation. The differential of this diffeomorphism is a valuable information for a numerical analysis of the imperfect bifurcation. The aim of this paper is to construct algorithms for a computation of . Singularity classes containing bifurcation points with , are considered.
Continuity of attractors
Dynamics and patterns of an activator-inhibitor model with cubic polynomial source
The dynamics of an activator-inhibitor model with general cubic polynomial source is investigated. Without diffusion, we consider the existence, stability and bifurcations of equilibria by both eigenvalue analysis and numerical methods. For the reaction-diffusion system, a Lyapunov functional is proposed to declare the global stability of constant steady states, moreover, the condition related to the activator source leading to Turing instability is obtained in the paper. In addition, taking the...
Eigenvalue questions on some quasilinear elliptic problems
Exact multiplicity of positive solutions to a superlinear problem.
Existence and bifurcation for some elliptic problems on exterior strip domains.
Existence and multiplicity of solutions to elliptic problems with discontinuities and free boundary conditions.
Existence of multiple solutions for a nonlinearly perturbed elliptic parabolic system in .
Existence of solutions for elliptic systems involving operators in divergence form.
Explicit construction, uniqueness, and bifurcation curves of solutions for a nonlinear Dirichlet problem in a ball.
Forced vibrations of wave equations with non-monotone nonlinearities
Formules et considérations diverses se rapportant à la théorie des ramifications
Four-parameter bifurcation for a -Laplacian system.
Funkcionální rovnice v nelineární analýze. Věnováno G. Prodimu, velkému učiteli a drahému příteli.
Generic properties of von Kármán equations
Global attractivity, oscillation and Hopf bifurcation for a class of diffusive hematopoiesis models
In this paper, we discuss the special diffusive hematopoiesis model with Neumann boundary condition. Sufficient conditions are provided for the global attractivity and oscillation of the equilibrium for Eq. (*), by using a new theorem we stated and proved. When P(t, χ) does not depend on a spatial variable χ ∈ Ω, these results are also true and extend or complement existing results. Finally, existence and stability of the Hopf bifurcation for Eq. (*) are studied.
Global bifurcation results for a semilinear biharmonic equation on all of .