Related papers: Nonlinear diffusion of dislocation density and sel…
This paper deals with the long-time behavior of solutions of nonlinear reaction-diffusion equations describing formation of morphogen gradients, the concentration fields of molecules acting as spatial regulators of cell differentiation in…
It has been shown in experiments that self-climb of prismatic dislocation loops by pipe diffusion plays important roles in their dynamical behaviors, e.g., coarsening of prismatic loops upon annealing, as well as the physical and mechanical…
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…
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 study invariant solutions of a certain class of time-fractional diffusion-wave equations with variable coefficients via Lie symmetry analysis. In physics, the fractional diffusion equation describes transport dynamics that are governed…
In this paper, we study a nonlinear boundary diffusion equation of porous medium type arising from a boundary control problem. We give a complete and sharp characterization of the asymptotic behavior of its solutions, and prove the…
This paper is devoted to the study of some nonlinear parabolic equations with discontinuous diffusion intensities. Such problems appear naturally in physical and biological models. Our analysis is based on variational techniques and in…
This paper is devoted to a fundamental solution of a nonlinear kinetic equation involving a porous medium or fast diffusion operator acting on velocities. Such a nonlinearity has interesting scaling properties, which result in a…
Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…
This paper focuses on the study of semilinear fractional diffusion-wave equations in the context of critical nonlinearities. Firstly, we address the issue of local well-posedness for the problem, examine spatial regularity, and the…
The nonlinear Schroedinger equation in the presence of disorder is considered. The dynamics of an initially localized wave packet is studied. A subdiffusive spreading of the wave packet is explained in the framework of a continuous time…
We study the existence and uniqueness of mild and strong solutions of nonlocal nonlinear diffusion problems of $p$-Laplacian type with nonlinear boundary conditions posed in metric random walk spaces. These spaces include, among others,…
One obtains a probabilistic representation for the entropic generalized solutions to a nonlinear Fokker-Planck equation in $\mathbb R^d$ with multivalued nonlinear diffusion term as density probabilities of solutions to a nonlinear…
In this paper we show some explicit results regarding non-linear diffusive equations on Poincar\'e half plane. We obtain exact solutions by using the generalized separation of variables and we also show the meaning of these results in the…
This paper compares two similar diffusion equations that appear in meteorology. One is the quasi-geostrophic equation, and the other is the convection-diffusion equation. Both are two-dimensional bilinear equations, and the order of…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
We study the long-time behavior of solutions to a class of evolution equations arising from random-time changes driven by subordinators. Our focus is on fractional diffusion equations involving mixed local and nonlocal operators. By…
This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state of zero stress and use linear semigroup theory to establish…
In this article we consider the discretely self-similar singular solutions of the Euler equations, and the possible velocity profiles concerned not only have decaying spatial asymptotics, but also have unconventional non-decaying…
We construct solutions of nonlinear reaction-diffusion equations with nonlinear boundary conditions in spaces where the problem is supercritical and show the nonlinear balance required between the nonlinear terms in order to obtain a…