Related papers: Existence, uniqueness and a priori estimates for a…
The paper is concerned with the principal eigenvalue of some linear elliptic operators with drift in two dimensional space. We provide a refined description of the asymptotic behavior for the principal eigenvalue as the drift rate…
The initial value problem P0, in all of the space, for the spatio - temporal FitzHugh - Nagumo equations is analyzed. When the reaction kinetics of the model can be outlined by means of piecewise linear approximations, then the solution of…
In this paper we introduce a model describing diffusion of species by a suitable regularization of a "forward-backward" parabolic equation. In particular, we prove existence and uniqueness of solutions, as well as continuous dependence on…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
This paper investigates the relations between the particular eigensolutions of a limiting functional differential equation of any order, which is the nominal (unperturbed) linear autonomous differential equations, and the associate ones of…
In the paper, the initial-boundary value problems to a semilinear integro-differential equation with multi-term fractional Caputo derivatives are analyzed. A particular case of this equation models oxygen diffusion through capillaries.…
In this paper, we deal with the initial value problem for a class of fully nonlinear parabolic equations with a singular Dirichlet boundary condition in one space dimension. The interior equation includes, for example, a fully nonlinear…
We study the problem of existence, uniqueness and regularity of probabilistic solutions of the Cauchy problem for nonlinear stochastic partial differential equations involving operators corresponding to regular (nonsymmetric) Dirichlet…
This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
This article focuses on parabolic equations with rough diffusion coefficients which are ill-posed in the classical sense of distributions due to the presence of a singular forcing. Inspired by the philosophy of rough paths and regularity…
It is studied the Cauchy problem for the equations of Burgers' type but with bounded dissipation flux. Such equations degenerate to hyperbolic ones as the velocity gradient tends to infinity. Thus the discontinuous solutions are permitted.…
Let $m\in \mathbb{N}$, $\alpha\in[0,1]$, and $V$ be a 1-periodic complex-valued distribution in the negative Sobolev space $H^{-m\alpha}[0,1]$. The singular non-self-adjoint eigenvalue problem $D^{2m}u+V u=\lambda u$, $D=-i d/dx$, with…
We study systems of nonlinear partial differential equations of parabolic type, in which the elliptic operator is replaced by the first order divergence operator acting on a flux function, which is related to the spatial gradient of the…
We analyze numerically a forward-backward diffusion equation with a cubic-like diffusion function, -emerging in the framework of phase transitions modeling- and its "entropy" formulation determined by considering it as the singular limit of…
We study the asymptotic behavior of solutions for the semilinear damped wave equation with variable coefficients. We prove that if the damping is effective, and the nonlinearity and other lower order terms can be regarded as perturbations,…
We study parabolic equations governed by integro-differential operators with nonlocal components in some directions and local components in the remaining directions. The setting contains the purely nonlocal, as well as the purely local…
We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends…
We introduce a new class of piece-wise quadratic potentials for nonlinear wave equations with a kink solutions. The potentials allow an exact description of the spectral properties for the linearized equation at the kink. This description…
We present in a detailed manner the scaling theory of irreversible aggregation characterized by the set of reaction rates $K(k,l)=1/k+1/l$, as well as a minor generalisation thereof. In this case, it is possible to evaluate the scaling…