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A class of semi-bounded solutions of the two-dimensional incompressible Euler equations satisfying either periodic or Dirichlet boundary conditions is examined. For smooth initial data, new blowup criteria in terms of the initial concavity…
The use of fully or partially absorbing boundary conditions for diffusion-based problems has become paradigmatic in physical chemistry and biochemistry to describe reactions occurring in solutions or in living media. However, as chemical…
The present work is devoted to the study of a boundary value problem for second order linear differential equation set on singular cylindrical domain. This problem can be regarded via a natural change of variables as an elliptic abstract…
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…
A kind of nonlocal reaction-diffusion equations on an unbounded domain containing fractional Laplacian operator is analyzed. To be precise, we prove the convergence of solutions of the equation governed by the fractional Laplacian to the…
In arXiv:2305.03945 [math.NA], a first-order optimization algorithm has been introduced to solve time-implicit schemes of reaction-diffusion equations. In this research, we conduct theoretical studies on this first-order algorithm equipped…
A perturbation series solution is constructed in terms of Airy functions for a nonlinear two-point boundary-value problem arising in an established model of steady electrodiffusion in one dimension, for two ionic species carrying equal and…
This work is concerned with numerically recovering multiple parameters simultaneously in the subdiffusion model from one single lateral measurement on a part of the boundary, while in an incompletely known medium. We prove that the boundary…
In this paper the asymptotic distributions are exactly solved for linearly independent solutions considering problems of the second order and for the coefficients of asymptotic destribution the recurent formulas are obtained. Further, using…
In this paper, the existence of smooth positive solutions to a Robin boundary-value problem with non-homogeneous differential operator and reaction given by a nonlinear convection term plus a singular one is established. Proofs chiefly…
We consider a singularly perturbed semilinear boundary value problem of a general form that allows various types of turning points. A solution decomposition is derived that separates the potential exponential boundary layer terms. The…
The aim of this paper is to study and classify the multiplicity of distinguished limits and asymptotic solutions for the advection equation with a general oscillating velocity field with the systematic use of the two-timing method. Our…
This paper is devoted to study the existence of solutions and the monotone method of second-order periodic boundary value problems when the lower and upper solutions $\alpha$ and $\beta$ violate the boundary conditions $…
This work explores the influence of domain size of a non-compact two dimensional annular domain on the evolution of pattern formation that is modelled by an \textit{activator-depleted} reaction-diffusion system. A closed form expression is…
We propose a method for the treatment of two--point boundary value problems given by nonlinear ordinary differential equations. The approach leads to sequences of roots of Hankel determinants that converge rapidly towards the unknown…
An initial-boundary value problem for the 1D self-adjoint parabolic equation on the half-axis is solved. We study a broad family of two-level finite-difference schemes with two parameters related to averagings both in time and space.…
This paper introduces a fast and numerically stable algorithm for the solution of fourth-order linear boundary value problems on an interval. This type of equation arises in a variety of settings in physics and signal processing. Our method…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
We present and analyze a discontinuous Petrov-Galerkin method with optimal test functions for a reaction-dominated diffusion problem in two and three space dimensions. We start with an ultra-weak formulation that comprises parameters…
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…