Methods for studying stability of systems with linear delay.
Minimum principle for quadratic spline collocation discretization of a convection-diffusion problem
Mixed type semicontinuous differential inclusions in Banach spaces
We consider a class of differential inclusions in (nonseparable) Banach spaces satisfying mixed type semicontinuity hypotheses and prove the existence of solutions for a problem with state constraints. The cases of dissipative type conditions and with time lag are also studied. These results are then applied to control systems.
Modelling tumour-immunity interactions with different stimulation functions
Tumour immunotherapy is aimed at the stimulation of the otherwise inactive immune system to remove, or at least to restrict, the growth of the original tumour and its metastases. The tumour-immune system interactions involve the stimulation of the immune response by tumour antigens, but also the tumour induced death of lymphocytes. A system of two non-linear ordinary differential equations was used to describe the dynamic process of interaction between the immune system and the tumour. Three different...
Multiple spatial scales in engineering and atmospheric low Mach number flows
The first part of this paper reviews the single time scale/multiple length scale low Mach number asymptotic analysis by Klein (1995, 2004). This theory explicitly reveals the interaction of small scale, quasi-incompressible variable density flows with long wave linear acoustic modes through baroclinic vorticity generation and asymptotic accumulation of large scale energy fluxes. The theory is motivated by examples from thermoacoustics and combustion. In an almost obvious way specializations of this...
Multiple spatial scales in engineering and atmospheric low Mach number flows
The first part of this paper reviews the single time scale/multiple length scale low Mach number asymptotic analysis by Klein (1995, 2004). This theory explicitly reveals the interaction of small scale, quasi-incompressible variable density flows with long wave linear acoustic modes through baroclinic vorticity generation and asymptotic accumulation of large scale energy fluxes. The theory is motivated by examples from thermoacoustics and combustion. In an almost obvious way specializations of...
Multiple-scale analysis for Painlevé transcendents with a large parameter
Multisummability of formal power series solutions of nonlinear meromorphic differential equations
In this paper a proof is given of a theorem of J. Écalle that formal power series solutions of nonlinear meromorphic differential equations are multisummable.
-widths for singularly perturbed problems
-widths for singularly perturbed problems
Kolmogorov -widths are an approximation theory concept that, for a given problem, yields information about the optimal rate of convergence attainable by any numerical method applied to that problem. We survey sharp bounds recently obtained for the -widths of certain singularly perturbed convection-diffusion and reaction-diffusion boundary value problems.
Nonlinear singularly perturbed systems of differential equations: A survey.
Nonlinear SPP with nonlocal boundary conditions and spectral approximation.
Nonlocal four-point boundary value problem for the singularly perturbed semilinear differential equations.
Non-standard dynamical systems. Shadows of trajectories and abstracts rivers.
Note on canonical forms for functional-differential equations.
Note on the asymptotic behavior of the solutions of differential equations with deviating arguments
Novel method for generalized stability analysis of nonlinear impulsive evolution equations
In this paper, we discuss some generalized stability of solutions to a class of nonlinear impulsive evolution equations in the certain piecewise essentially bounded functions space. Firstly, stabilization of solutions to nonlinear impulsive evolution equations are studied by means of fixed point methods at an appropriate decay rate. Secondly, stable manifolds for the associated singular perturbation problems with impulses are compared with each other. Finally, an example on initial boundary value...
Numerical experiments with different schemes for a singularly perturbed problem.
Numerical solution of initial and singularly perturbed two-point boundary value problems using adaptive spline function approximation.
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