相关论文: Local strong solutions in a quasilinear Moore-Gibs…

We study the quasistatic evolution of a linear peridynamic Kelvin-Voigt viscoelastic material. More specifically, we consider the gradient flow of a nonlocal elastic energy with respect to a nonlocal viscous dissipation. Following an…

We prove a new linearization principle for the nonlinear stability of solutions to semilinear evolution equations of parabolic type. We assume that the set of equilibria forms a finite dimensional manifold of normally stable and normally…

The classical system of shallow-water (Saint--Venant) equations describes long surface waves in an inviscid incompressible fluid of a variable depth. Although shock waves are expected in this quasilinear hyperbolic system for a wide class…

Some solutions for one class of nonlinear fourth-order partial differential equations \[u_{tt} = ({\kappa u + \gamma u^2})_{xx} + \nu uu_{xxxx} + \mu u_{xxtt} + \alpha u_x u_{xxx} + \beta u_{xx}^2 \] where $\alpha ,\;\beta ,\;\gamma ,\;\mu…

In this paper we study several aspects related with solutions of nonlocal problems whose prototype is $$ u_t =\displaystyle \int_{\mathbb{R}^N} J(x-y) \big( u(y,t) -u(x,t) \big) \mathcal G\big( u(y,t) -u(x,t) \big) dy \qquad \mbox{ in } \,…

Reaction-diffusion equations have several applications in the field of population dynamics and some of them are characterized by the presence of a factor which describes different types of food sources in a heterogeneous habitat. In this…

In this paper we study the parabolic evolution equation $\partial_t u=(|Du|^{2}+2|\det Du|)^{-1} \Delta u$, where $u : M\times[0,\infty) \to N$ is an evolving map between compact flat surfaces. We use a tensor maximum principle for the…

We establish the local continuity of locally bounded weak solutions (temperatures) to the doubly singular parabolic equation modeling the phase transition of a material: \[ \partial_t \beta(u)-\Delta_p u\ni 0\quad\text{ for…

We investigate the existence of strong solutions to a general class of doubly multivalued and nonlinear evolution equations of second order. The multivalued operators are generated by the subdifferential of nonsmooth potentials that live in…

This paper studies the asymptotic behavior of solutions of the parabolic-parabolic chemotaxis model with logistic-type sources in heterogeneous bounded domains: \begin{equation*} \label{u-v-eq00} \begin{cases} u_t=\Delta u-\chi\nabla\cdot…

We study a nonlocal version of the two-phase Stefan problem, which models a phase transition problem between two distinct phases evolving to distinct heat equations. Mathematically speaking, this consists in deriving a theory for…

The aim of this paper is to provide a comprehensive study of some linear nonlocal diffusion problems in metric measure spaces. These include, for example, open subsets in $\mathbb{R}^N$, graphs, manifolds, multi-structures or some fractal…

We derive the evolution equation for the density matrix of a UV- and IR- limited band of comoving momentum modes of the canonically normalized scalar degree of freedom in two examples of nearly de Sitter universes. Including the effects of…

We are concerned with Dirichlet problems of the form $${\mathop{\rm div}\nolimits} (|D u|^{p-2}Du)+f(u)=0\ \mbox{ in }\Omega,\qquad u=0\ \mbox{ on }\partial\Omega, $$ where $\Omega$ is a bounded domain of $\mathbb{R}^n$, $n\ge 2$, $1<p<n$…

We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…

This paper establishes the emergence of slowly moving transition layer solutions for the $p$-Laplacian (nonlinear) evolution equation, \[ u_t = \varepsilon^p(|u_x|^{p-2}u_x)_x - F'(u), \qquad x \in (a,b), \; t > 0, \] where $\varepsilon>0$…

We consider the potentially degenerate haptotaxis system \begin{equation*} \left\{ \begin{aligned} u_t &= \nabla \cdot (\mathbb{D} \nabla u + u \nabla \cdot \mathbb{D}) - \chi \nabla \cdot (u\mathbb{D}\nabla w) + \mu u(1-u^{r- 1}), \\ w_t…

The low-temperature normal-state specific heat and resistivity curves of various nonmagnetic intermetallic compounds manifest an anomalous thermal evolution. Such an anomaly is exhibited as a break in the slope of the linearized C/T versus…

We concern a family $\{(u_{\varepsilon},v_{\varepsilon})\}_{\varepsilon > 0}$ of solutions of the Lane-Emden system on a smooth bounded convex domain $\Omega$ in $\mathbb{R}^N$ \[\begin{cases} -\Delta u_{\varepsilon} = v_{\varepsilon}^p…

We propose an evolution equation for unintegrated gluon densities that is valid for large values of the QCD coupling constant $\bar{\alpha} _s$. Our approach is based on the linear resummation model introduced by Sta\'{s}to. We generalize…