Related papers: Existence, uniqueness and a priori estimates for a…
We consider an evolution equation of parabolic type in R having a travelling wave solution. We perform an appropriate change of variables which transforms the equation into a non local evolution one having a travelling wave solution with…
In this note we provide some precise estimates explaining the diffusive structure of partially dissipative systems with time-dependent coefficients satisfying a uniform Kalman rank condition. Precisely, we show that under certain (natural)…
This work obtains a fixed-point equation for the solution of linear parabolic partial differential problems based on solutions to heat problems. This is a pointwise equality, so we have required non-standard techniques that involve the…
We present mathematical proofs on the existence and uniqueness of weak solutions for a special class of non linear parabolic and hyperbolic equations of mathematical physics subject to colored noise (structured turbulence) as random-…
We investigate in this paper a scalar reaction diffusion equation with a nonlinear reaction term depending on x-ct. Here, c is a prescribed parameter modelling the speed of climate change and we wonder whether a population will survive or…
Aim of this paper is the qualitative analysis of a boundary value problem for a third order non linear parabolic equation which describes several dissipative models. When the source term is linear, the problem is explictly solved by means…
This paper investigates oscillation-free stability conditions of numerical methods for linear parabolic partial differential equations with some example extrapolations to nonlinear equations. Not clearly understood, numerical oscillations…
In this paper we characterise the global stability, global boundedness and recurrence of solutions of a scalar nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable autonomous…
We investigate inverse boundary problems associated with a time-dependent semilinear hyperbolic equation, where both nonlinearity and sources (including initial displacement and initial velocity) are unknown. We establish in several generic…
We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished as t tends to infinity, the first being a regime ahead of the…
The paper is concerned with the effect of the spatio-temporal heterogeneity on the principal eigenvalue of some linear time-periodic parabolic system. Various asymptotic behaviors of the principal eigenvalue and its monotonicity, as a…
We exhibit a class of singularly perturbed parabolic problems which the asymptotic behavior can be described by a system of ordinary differential equation. We estimate the convergence of attractors in the Hausdorff metric by rate of…
This article provides a brief introduction to the a posteriori error analysis of parabolic partial differential equations, with an emphasis on challenges distinct from those of steady-state problems. Using the heat equation as a model…
In this paper we study a class of nonlinear anisotropic parabolic problems in bounded domains. In detail, we study the influences of the initial data and the forcing term f on the behavior of the solutions. We prove existence and uniqueness…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on $\mathbb{R}^d$. Using the properties of the…
We study existence and stability of travelling waves for nonlinear convection diffusion equations in the 1-D Euclidean space. The diffusion coefficient depends on the gradient in analogy with the p-Laplacian and may be degenerate.…
We consider parabolic systems with nonlinear dynamic boundary conditions, for which we give a rigorous derivation. Then, we give them several physical interpretations which includes an interpretation for the porous-medium equation, and for…
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…
We study parabolic equations in variable H\"older spaces on domains of Euclidean spaces. The existence and uniqueness of solutions is proved.