Related papers: Global Existence and Regularity Results for Strong…
We analyze semilinear reaction-diffusion systems that are mass controlled, and have nonlinearities that satisfy critical growth rates. The systems under consideration are only assumed to satisfy natural assumptions, namely the preservation…
This paper provides two results that are useful in the study of the existence and the stability properties of a periodic solution for a given dynamical system. The first result deals with scalar time-periodic systems and establishes the…
We study a hyperbolic-parabolic model of chemotaxis in dimensions one and two. In particular, we prove the global existence of classical solutions in certain dissipation regimes.
We establish partial regularity for vector-valued solutions to parabolic systems where the coefficients are possibly discontinuous with respect to (x,t). More precisely, we assume a VMO-condition with respect to the (x,t) and continuity…
In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction-diffusion systems posed in a bounded domain of $\mathbb{R}^N$. The nonlinear reactive terms are assumed to satisfy natural…
In this work there is established an optimal existence and regularity theory for second order linear parabolic differential equations on a large class of noncompact Riemannian manifolds. Then it is shown that it provides a general unifying…
Our goal in this paper is to prove the global existence of a classical solution for the isentropic nozzle flow. Regarding this problem, there exist some global existence theorems of weak solutions. However, that of classical solutions does…
We present a new, short proof of the increased regularity obtained by solutions to uniformly parabolic partial differential equations. Though this setting is fairly introductory, our new method of proof, which uses a priori estimates, can…
We study the global existence of classical solutions to volume-surface reaction-diffusion systems with control of mass. Such systems appear naturally from modeling evolution of concentrations or densities appearing both in a volume domain…
This paper considers quadratic and super-quadratic reaction-diffusion systems for reversible chemistry, for which all species satisfy uniform-in-time $L^1$ a-priori estimates, for instance, as a consequence of suitable mass conservation…
We prove the existence of infinitely many classical periodic solutions for a class of semilinear wave equations with periodic boundary conditions. Our argument relies on some new estimates for the linear problem with periodic boundary…
We present a local almost everywhere regularity result for a general nonlinear non-diagonal parabolic system, which main part depends on symmetric part of the gradient.
In this paper, we study the global existence and asymptotic behavior of classical solutions near vacuum for the initial-boundary value problem modeling isentropic supersonic flows through divergent ducts. The governing equations are the…
We address the question whether Bohmian trajectories exist for all times. Bohmian trajectories are solutions of an ordinary differential equation involving a wavefunction obeying either the Schroedinger or the Dirac equation. Some…
We prove the existence and uniqueness of solutions for a family of nonlinear parabolic systems related to phase field models taking in account variations of temperature and the possibility of a general class of nonlinearities. The present…
In this work, we investigate the dynamics of an inhomogeneous coupled nonlinear Schrodinger system with quadratic-type interactions. Such systems arise naturally in nonlinear dynamics and mathematical physics, particularly in nonlinear…
The global existence of classical solutions to reaction-diffusion systems in arbitrary space dimensions is studied. The nonlinearities are assumed to be quasi-positive, to have (slightly super-) quadratic growth, and to possess a mass…
We prove existence of infinitely many classical periodic solutions with periodic boundary conditions for a class of monotone semilinear wave equations. Our argument relies on some new estimates for the linear problem with periodic boundary…
For a class of quasilinear parabolic systems with nonlinear Robin boundary conditions we construct a compact local solution semiflow in a nonlinear phase space of high regularity. We further show that a priori estimates in lower norms are…
We prove global existence for quasilinear wave equations outside of a wide class of obstacles. The obstacles may contain trapped hyperbolic rays as long as there is local exponential energy decay for the associated linear wave equation.…