scientific article; zbMATH DE number 734932

Leonid V. Kalachev, V. F. Butuzov, A. B. Vasil'eva

Publication date: 19 March 1995

Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.

periodic solutions asymptotic expansion singular perturbations combustion transition layers reaction-diffusion equations singularly perturbed problems boundary and interior layers FitzHugh-Nagumo system dissipative structures semiconductor devices boundary layer functions method of Vishik-Lyusternik

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Singular perturbations for ordinary differential equations (34E15) Research exposition (monographs, survey articles) pertaining to partial differential equations (35-02) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

Related Items

Shadow limit using renormalization group method and center manifold method, Blockwise estimate of the fundamental matrix of linear singularly perturbed differential systems with small delay and its application to uniform asymptotic solution, Asymptotics and attractors for quasilinear parabolic-hyperbolic systems governing the motions of heavily burdened deformable bodies, Projector approach to the Butuzov-Nefedov algorithm for asymptotic solution of a class of singularly perturbed problems in a critical case, A class of singularly perturbed delayed boundary value problem in the critical case, A parameter robust numerical method for a system of two singularly perturbed convection-diffusion equations, Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solutions, Step-like contrast structure for a quasilinear system of singularly perturbed differential equations with a zero characteristic number, Transitions in a Duffing oscillator excited by random noise, Finite-Horizon $$H_{\infty }$$ Control Problem with Singular Control Cost, Elliptic regularization for the semi-linear telegraph system, Singularly perturbed semilinear elliptic boundary value problems with discontinuous source term, A one-dimensional reaction/diffusion system with a fast reaction, Delay-dependent passivity and passification for uncertain singularly perturbed Markovian jump systems with time-varying delay, Asymptotic behaviour of three-dimensional singularly perturbed convection-diffusion problems with discontinuous data, Existence and asymptotic representation of the autowave solution of a system of equations, Closure method and asymptotic expansions for linear stochastic systems, Chattering as a singular problem, Modulational instability in the nonlocal $\chi ^{(2)}$-model, Asymptotic solution of the singularly perturbed infinite dimensional Riccati equation, Lions regularization of the telegraph system with nonlinear boundary conditions, Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems. I: Reaction-diffusion type, Relaxation oscillations in spruce-budworm interactions, Order reduction of a non-Lipschitzian model of monodisperse spray ignition, Existence of a periodic solution in the form of a two-dimensional front in a system of parabolic equations, The Bogner-Fox-Schmit element finite volume methods on the Shishkin mesh for fourth-order singularly perturbed elliptic problems, Unnamed Item, The dynamics of pasture-herbivores-carnivores with sigmoidal density dependent harvesting, Elliptic-like regularization of a fully nonlinear evolution inclusion and applications, Asymptotic expansion for the solution of singularly perturbed delay differential equations, Asymptotic solutions of singularly perturbed differential algebraic equations with turning points, Connecting orbits near the adiabatic limit of Lagrangian systems with turning points, Data based quantification of synchronization, A Novel Approach to Exact Slow-Fast Decomposition of Linear Singularly Perturbed Systems with Small Delays, Invariant manifolds for random dynamical systems with slow and fast variables, Dynamics of self-excited generators with diverse nonlinear delayed feedbacks, Asymptotic approximations for solutions of Sturm-Liouville differential equations with a large complex parameter and nonsmooth coefficients, Eight Perspectives on the Exponentially Ill-Conditioned Equation $\varepsilon y - x y' + y = 0$, Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion-advection equation, Modeling of Excitatory Amino Acid Transporters, An asymptotic study of the inductive pattern formation mechanism in Drosophila egg development, Application of vibrational control to linear-quadratic control problems., The motion of a particle on a light viscoelastic bar: asymptotic analysis of its quasilinear parabolic-hyperbolic equation., Asymptotic solutions of singular perturbed problems with an instable spectrum of the limiting operator, Saddle-point equilibrium sequence in one class of singular infinite horizon zero-sum linear-quadratic differential games with state delays, Singular perturbation analysis of a stationary diffusion/reaction system whose solution exhibits a corner-type behavior in the interior of the domain., Existence and stability of periodic contrast structure in reaction-advection-diffusion equation with discontinuous reactive and convective terms, A global uniformly convergent finite element method for a quasi-linear singularly perturbed elliptic problem, Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem, Global uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Higher-order elements, First asymptotic approximations to a solution of singularly perturbed optimal control problem with intersecting solutions of degenerate problem, Asymptotic solution of a singularly perturbed optimal problem with integral constraint, Differentiability and its asymptotic analysis for nonlinear singularly perturbed boundary value problem, Multiple time scales and perturbation methods for high frequency electromagnetic-hydrodynamic coupling in the treatment of liquid metals, Elliptic-like regularization of semilinear evolution equations and applications to some hyperbolic problems, Time-periodic boundary layer solutions to singularly perturbed parabolic problems, Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions, A steplike contrast structure in a singularly perturbed system of elliptic equations, A regularized iterative scheme for solving singularly perturbed elliptic PDE, Singular perturbation analysis and gene regulatory networks with delay, Asymptotic analysis of dissolution of a spherical bubble (case of fast reaction outside the bubble), Singularly perturbed elliptic problems in the case of exchange of stabilities, Robust error estimation in energy and balanced norms for singularly perturbed fourth order problems, A singularly perturbed differential equation with piecewise constant argument of generalized type, Asymptotic behavior of the solutions of differential equations with double singularity in a conditionally stable case, Iteration method of approximate solution of the Cauchy problem for a singularly perturbed weakly nonlinear differential equation of an arbitrary order, Singularly perturbed second order semilinear boundary value problems with interface conditions, Suboptimal solution of a cheap control problem for linear systems with multiple state delays, Singularly perturbed periodic parabolic equations with alternating boundary layer type solutions, Asymptotic approximations for a singularly perturbed convection-diffusion problem with discontinuous data in a sector, Uniform stabilizability of parameter-dependent systems with state and control delays by smooth-gain controls, Nonlinear aspects of high Reynolds number channel flows, Asymptotic integration of singularly perturbed differential algebraic equations with turning points. I, Contrast structure for singular singularly perturbed boundary value problem, Elliptic regularizations for the nonlinear heat equation, Global pointwise error estimates for uniformly convergent finite element methods for the elliptic boundary layer problem, Fast-slow dynamics in first-order initial value problems with slowly varying parameters and application to a harvested logistic model, Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems: Convection-diffusion type, Projector approach to constructing asymptotic solution of initial value problems for singularly perturbed systems in critical case, Asymptotic approximation to a solution of a singularly perturbed linear-quadratic optimal control problem with second-order linear ordinary differential equation of state variable, Modeling of excitatory amino acid transporters and clearance of synaptic cleft on millisecond time scale, On step-like contrast structure of singularly perturbed systems, Asymptotics of the solution to a stationary piecewise-smooth reaction-diffusion equation with a multiple root of the degenerate equation, A singularly perturbed semilinear reaction-diffusion problem in a polygonal domain, Initial boundary value problem for a singularly perturbed parabolic equation in case of exchange of stability, Conditionally stable case for boundary-value problem with double singularity, Existence and stability of periodic solution of contrast structure type in discontinuous singularly perturbed reaction-convection-diffusion problem, Numerical exploration of a system of reaction-diffusion equations with internal and transient layers, Maximum norm error analysis of a 2d singularly perturbed semilinear reaction-diffusion problem, Asymptotic analysis of magnetic induction with high frequency for solid conductors, $H_\infty$ control of linear singularly perturbed systems with small state delay, Give your ODEs a singular perturbation!, Singularly perturbed partly dissipative reaction-diffusion systems in case of exchange of stabilities., Order reduction for an RNA virus evolution model, Step-like contrast structure in a singularly perturbed system of parabolic equations, An averaging method for singularly perturbed systems of semilinear differential inclusions with analytic semigroups, Stability and stabilization of one class of three time-scale systems with delays