Related papers: Global Existence and Regularity Results for Large …
We study the global existence and space-time asymptotics of solutions for a class of nonlocal parabolic semilinear equations. Our models include the Nernst-Planck and the Debye-Hukel drift-diffusion systems as well as parabolic-elliptic…
This paper is devoted to the analysis of non-negative solutions for a degenerate parabolic-elliptic Patlak-Keller-Segel system with critical nonlinear diffusion in a bounded domain with homogeneous Neumann boundary conditions. Our aim is to…
We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle,…
This work analyzes a predator-prey cross-diffusion system coupled with two chemical substances under homogeneous Neumann boundary conditions in a bounded domain Omega subset of R^n (n >= 2) with smooth boundary dOmega. Under appropriate…
We consider general multi-species models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on…
We prove global existence of solutions to quasilinear wave equations with quadratic nonlinearities exterior to nontrapping obstacles in spatial dimensions four and higher. This generalizes a result of Shibata and Tsutsumi in spatial…
We consider reaction-diffusion equations on the planar square lattice that admit spectrally stable planar travelling wave solutions. We show that these solutions can be continued into a branch of travelling corners. As an example, we…
There is little analytical theory for the behavior of solutions of the Kuramoto-Sivashinsky equation in two spatial dimensions over long times. We study the case in which the spatial domain is a two-dimensional torus. In this case, the…
We study the global existence of solutions to a one-dimensional drift-diffusion equation with logistic term, generalizing the classical parabolic-elliptic Keller-Segel aggregation equation arising in mathematical biology. In particular, we…
We prove global existence and scattering for a class of quadratic Schrodinger equations in dimension 2. The proof relies on the idea of space-time resonance.
The global existence of classical solutions to strongly coupled parabolic systems is shown to be equivalent to the availability of an iterative scheme producing a sequence of solutions with uniform continuity in the BMO norms. Amann's…
This work is devoted to present Massera-type theorems for the Kawahara system, a higher order dispersive equation, posed in a bounded domain. Precisely, thanks to some properties of the semigroup and the decays of the solutions of this…
This paper studies the asymptotic behavior of coexistence steady states of the Shigesada-Kawasaki-Teramoto model as both cross-diffusion coefficients tend to infinity at the same rate. In the case when either one of two cross-diffusion…
We consider a class of cross diffusion systems with degenerate (or porous media type) diffusion which is inspired by models in mathematical biology/ecology with zero self diffusions. Known techniques for scalar equations are no longer…
We consider the Kuramoto-Sivashinsky equation (KSE) on the two-dimensional torus in the presence of advection by a given background shear flow. Under the assumption that the shear has a finite number of critical points and there are…
In this paper we prove global existence for solutions of the Vlasov-Poisson system in convex bounded domains with specular boundary conditions and with a prescribed outward electrical field at the boundary.
We prove the local and global in time existence of the classical solutions to two general classes of the stress-assisted diffusion systems. Our results are applicable in the context of the non-Euclidean elasticity and liquid crystal…
The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy…
Global existence and scattering for the nonlinear defocusing Schr\"odinger equation in 2 dimensions are known for domains exterior to star-shaped obstacles and for nonlinearities that grow at least as the quintic power. In this paper, we…
Global existence is established for classical solutions to a chemotaxis model with signal-dependent motility for a general class of motility functions $\gamma$ which may in particular decay in an arbitrary way at infinity. Assuming further…