Related papers: Analytic regularity for a singularly perturbed rea…
We consider a singularly perturbed reaction diffusion problem as a first order two-by-two system. Using piecewise discontinuous polynomials for the first component and $H_{div}$-conforming elements for the second component we provide a…
We study a two-point boundary value problem for a linear differen\-tial-algebraic equation with constant coefficients by using the method of parameterization. The parameter is set as the value of the continuously differentiable component of…
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
In this paper, a class of linear parabolic singularly perturbed second order differential equations of reaction-diffusion type with initial and Robin boundary conditions is considered. The solution u of this equation is smooth, whereas the…
This article concerns second-order time discretization of subdiffusion equations with time-dependent diffusion coefficients. High-order differentiability and regularity estimates are established for subdiffusion equations with…
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regular exponential boundary layers appear in the solution. A…
We consider linear reaction--diffusion problems with mixed Diriclet-Neumann-Robin conditions. The diffusion matrix, reaction coefficient, and the coefficient in the Robin boundary condition are defined with an uncertainty which allow…
We consider a system of two singularly perturbed Boundary Value Problems (BVPs) of convection-diffusion type with discontinuous source terms and a small positive parameter multiplying the highest derivatives. Then their solutions exhibit…
Recently, the problem of boundary stabilization for unstable linear constant-coefficient reaction-diffusion equation on N-balls has been solved by means of the backstepping method. However, the extension of this result to spatially-varying…
In this paper we are concerned with a two-penalty boundary obstacle problem of interest in thermics, fluid dynamics and electricity. Specifically, we prove existence, uniqueness and optimal regularity of the solutions, and we establish…
We undertake a detailed analysis of a reaction-advection-diffusion (RAD) equation from the viewpoint of pulse-response studies, with particular attention to effects due to the advection velocity. Our boundary-value problem is a mathematical…
The time-fractional diffusion equation is considered, where the time derivative is either of Caputo or Riemann-Liouville type. The solution of a general initial-boundary value problem with time-dependent boundary conditions over bounded and…
This paper focuses on the initial- and boundary-value problem for the two-dimensional micropolar equations with only angular velocity dissipation in a smooth bounded domain. The aim here is to establish the global existence and uniqueness…
We revisit a textbook example of a singularly perturbed nonlinear boundary-value problem. Unexpectedly, it shows a wealth of phenomena that seem to have been overlooked previously, including a pitchfork bifurcation in the number of…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified which matches the discontinuity in the initial condition. The…
A class of different schemes for the numerical solving of semilinear singularly--perturbed reaction--diffusion boundary--value problems was constructed. The stability of the difference schemes was proved, and the existence and uniqueness of…
In the present paper we consider the numerical solving of a semilinear singular--perturbation reaction--diffusion boundary--value problem having boundary layers. A new difference scheme is constructed, the second order of convergence on a…
A semilinear singularly perturbed reaction-diffusion equation with Dirichlet boundary conditions is considered in a convex unbounded sector. The singular perturbation parameter is arbitrarily small, and the "reduced equation" may have…
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the…
Mathematical modeling of many physical processes such as diffusion, viscosity of fluids and combustion involves differential equations with small coefficients of higher derivatives. These may be small diffusion coefficients for modeling the…