Related papers: Diffusion toward non-overlapping partially reactiv…
An integro differential equation which is able to describe the evolution of a large class of dissipative models, is considered. By means of an equivalence, the focus shifts to the perturbed sine- Gordon equation that in superconductivity…
Semi-Lagrangian methods have traditionally been developed in the framework of hyperbolic equations, but several extensions of the Semi-Lagrangian approach to diffusion and advection--diffusion problems have been proposed recently. These…
A hybrid asymptotic-numerical method is presented for obtaining the full probability distribution of capture times of a random walker by multiple small traps located inside a bounded two-dimensional domain with reflective boundaries. As…
The goal of this work is to establish the global existence of nonnegative classical solutions in all dimensions for a system of highly nonlinear reaction-diffusion equations. We address the case for different diffusion coefficients and the…
Diffusion through semipermeable structures arises in a wide range of processes in the physical and life sciences. Examples at the microscopic level range from artificial membranes for reverse osmosis to lipid bilayers regulating molecular…
We propose threshold diffusion processes as unique solutions to stochastic differential equations with step-function coefficients, and obtain explicit expressions for the conditional Laplace transform of the hitting times and the potential…
We study the long-time asymptotics of prototypical non-linear diffusion equations. Specifically, we consider the case of a non-degenerate diffusivity function that is a (non-negative) polynomial of the dependent variable of the problem. We…
We establish asymptotic diffusion limits of the non-classical transport equation derived in [E. W. Larsen, A generalized Boltzmann equation for non-classical particle transport, Joint international topical meeting on mathematics &…
The Neumann boundary problem for the perturbed sine-Gordon equation describing the electrodynamics of Josephson junctions has been considered. The behavior of a viscous term, described by a higher-order derivative with small diffusion…
Exterior Dirichlet problems for two-dimensional lattice waves on the semi-infinite triangular lattice are considered. Namely, we study Dirichlet problems for the two-dimensional discrete Helmholtz equation in a plane with a hole. New…
We propose an analytical method for understanding the problem of long range electron transfer reaction in solution, modeled by a particle undergoing diffusive motion under the influence of many potentials which are involved (donor - bridge…
We study Lorentz processes in two different settings. Both cases are characterized by infinite expectation of the free-flight times, contrary to what happens in the classical Gallavotti-Spohn models. Under a suitable Boltzmann-Grad type…
We propose an analytical framework to model the effect of single and multiple mechanical surface oscillators on the dynamics of vertically polarized elastic waves propagating in a semi-infinite medium. The formulation extends the canonical…
Circular domains frequently appear in the fields of ecology, biology and chemistry. In this paper, we investigate the equivariant Hopf bifurcation of partial functional differential equations with Neumann boundary condition on a…
We show that the boundary behaviour of solutions to nonlocal fractional equations posed in bounded domains strongly differs from the one of solutions to elliptic problems modelled upon the Laplace-Poisson equation with zero boundary data.…
Sub-diffusion equations are used in a large range of applications including fluids, plasma physics and biology. Their mathematical analysis is advanced even if a much larger literature addresses super-diffusions. The goal of this paper is…
We present a numerical method for the solution of diffusion problems in unbounded planar regions with complex geometries of absorbing and reflecting bodies. Our numerical method applies the Laplace transform to the parabolic problem,…
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…
We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features…
By working with the periodic resolvent kernel and Bloch-decomposition, we establish pointwise bounds for the Green function of the linearized equation associated with spatially periodic traveling waves of a system of reaction diffusion…