Related papers: Convergence in the Boundary Layer for Nonhomogeneo…
The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…
Late-lumping feedback design for infinite-dimensional linear systems with unbounded input operators is considered. The proposed scheme is suitable for the approximation of backstepping and flatness-based designs and relies on a…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…
This manuscript presents a new extended linear system for integral equation based techniques for solving boundary value problems on locally perturbed geometries. The new extended linear system is similar to a previously presented technique…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
The nonlocal models of peridynamics have successfully predicted fractures and deformations for a variety of materials. In contrast to local mechanics, peridynamic boundary conditions must be defined on a finite volume region outside the…
We consider Lie and Strang splitting for the time integration of constrained partial differential equations with a nonlinear reaction term. Since such systems are known to be sensitive with respect to perturbations, the splitting procedure…
We study a control system resembling a singularly perturbed system whose variables are decomposed into groups that change their values with rates of different orders of magnitude. We establish that the slow trajectories of this system are…
In this study we consider perturbative series solution with respect to a parameter {\epsilon} > 0. In this methodology the solution is considered as an infinite sum of a series of functional terms which usually converges fast to the exact…
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential…
Generally, natural scientific problems are so complicated that one has to establish some effective perturbation or nonperturbation theories with respect to some associated ideal models. In this Letter, a new theory that combines…
In this paper, an idea to solve nonlinear equations is presented. During the solution of any problem with Newton's Method, it might happen that some of the unknowns satisfy the convergence criteria where the others fail. The convergence…
We prove existence and uniqueness of nonnegative solutions for a nonlocal in time integrodifferential diffusion system related to angiogenesis descriptions. Fundamental solutions of appropriately chosen parabolic operators with bounded…
Consider a linear impulsive equation in a Banach space $$\dot{x}(t)+A(t)x(t) = f(t), ~t \geq 0,$$ $$x(\tau_i +0)= B_i x(\tau_i -0) + \alpha_i,$$ with $\lim_{i \rightarrow \infty} \tau_i = \infty $. Suppose each solution of the corresponding…
In this paper, we present an approach to characterising fast-reaction limits of systems with nonlinear diffusion, when there are either two reaction-diffusion equations, or one reaction-diffusion equation and one ordinary differential…
In this work we study the behavior of a family of solutions of a semilinear elliptic equation, with homogeneous Neumann boundary condition, posed in a two-dimensional oscillating thin region with reaction terms concentrated in a…
We study the numerical approximation of time-dependent, possibly degenerate, second-order Hamilton-Jacobi-Bellman equations in bounded domains with nonhomogeneous Dirichlet boundary conditions. It is well known that convergence towards the…
The divergence condition is reformulated in the scaled boundary coordinates so as to prevent the spurious solutions in the finite element formulation.
This paper introduces a novel approach to system identification for nonlinear input-output models that minimizes the simulation error and frames the problem as a constrained optimization task. The proposed method addresses vanishing…
Localisation limits and nonlocal approximations of degenerate parabolic systems have experienced a renaissance in recent years. However, only few results cover anisotropic systems. This work addresses this gap by establishing the…