相关论文: An example of global classical solution for the Pe…
We consider a collisionless ensemble of classical particles coupled to a Klein-Gordon field. For the resulting nonlinear system of partial differential equations, the relativistic Vlasov-Klein-Gordon system, we prove local-in-time existence…
In this paper, we consider the nonlinear Schr\"odinger equation, $$ i\partial_{t}u+\Delta u= \mu|u|^p u, \quad (t,x)\in \mathbb{R}^{d+1}, $$ with $\mu=\pm1, p>0$. In this work, we consider the mass-subcritical cases, that is, $p\in…
In this paper we study the Dirichlet problem of translating mean curvature equations over domains in Riemannian manifolds with dimension $n$. Imitating the generalized solution theory of Miranda-Giusti, we define a new conformal area…
The Cauchy problem is studied for very general systems of evolution equations, where the time derivative of solution is written by Fourier multipliers in space and analytic nonlinearity, with no other structural requirement. We construct a…
Consider the Cauchy problem for the radial cubic wave equation in 1+3 dimensions with either the focusing or defocusing sign. This problem is critical in $\dot{H}^{\frac{1}{2}} \times \dot{H}^{-\frac{1}{2}}$ and subcritical with respect to…
We consider the Cauchy problem for the wave equation on a non-globally hyperbolic manifold of the special form (Minkowski plane with a handle) containing closed timelike curves (time machines). We prove that the classical solution of the…
We consider the Cauchy problem in $\mathbb{R}^n,$ $n\geq 1,$ for a semilinear damped wave equation with nonlinear memory. Global existence and asymptotic behavior as $t\rightarrow\infty$ of small data solutions have been established in the…
We consider classical solutions to the chemotaxis system with logistic source $f(u) := au-\mu u^2$ under nonlinear Neumann boundary condition $\frac{\partial u}{ \partial \nu } = |u|^{p}$ with $p>1$ in a smooth convex bounded domain $\Omega…
We study whether the solutions of a parabolic equation with diffusion given by the fractional Laplacian and a dominating gradient term satisfy Dirichlet boundary data in the classical sense or in the generalized sense of viscosity…
We formulate on rectangles and on the right horizontal half-strip initial-boundary value problems for a two-dimensional Benney-Lin type equation. Existence and uniqueness of a regular solution as well as the exponential decay rate for the…
We study the Cauchy Problem for the relativistic Boltzmann equation with near Vacuum initial data. Unique global in time "mild" solutions are obtained uniformly in the speed of light parameter $c \ge 1$. We furthermore prove that solutions…
In this paper, we consider the Cauchy problem of the multi-dimensional generalized MHD system in the whole space and construct global smooth solutions with a class of large initial data by exploring the structure of the nonlinear term.…
We study the Cauchy problem of higher dimensional Einstein-Maxwell-Higgs system in the framework of Bondi coordinates. As a first step, the problem is reduced to a single first-order integro-differential equation by defining a generalized…
In this paper we investigate the Cauchy problem of d-dimensional Euler-Poincar\'{e} equations. By choosing a class of new and special initial data, we can transform this d-dimensional Euler-Poincar\'{e} equations into the Camassa-Holm type…
Solutions to the Cauchy problem for the one-dimensional cubic nonlinear Schr\"odinger equation on the real line are studied in Sobolev spaces $H^s$, for $s$ negative but close to 0. For smooth solutions there is an {\em a priori} upper…
In this article we present some results on the existence of positive and ground state solutions for the nonlinear Klein-Gordon-Maxwell equations. We introduce a general nonlinearity with subcritical and supercritical growth which does not…
The Cauchy problem for the compressible flow of nematic liquid crystals in the framework of critical spaces is considered. We first establish the existence and uniqueness of global solutions provided that the initial data are close to some…
We study the global structure of the set of radial solutions of a nonlinear Dirichlet problem involving the p-Laplacian with p>2, in the unit ball of $R^N$, $N \ges 1$. We show that all non-trivial radial solutions lie on smooth curves of…
The asymptotic behaviour of vacuum Bianchi models of class A near the initial singularity is studied, in an effort to confirm the standard picture arising from heuristic and numerical approaches by mathematical proofs. It is shown that for…
Let $1<p<+\infty$ and let $\Omega\subset\mathbb R^N$ be either a ball or an annulus. We continue the analysis started in [Boscaggin, Colasuonno, Noris, ESAIM Control Optim. Calc. Var. (2017)], concerning quasilinear Neumann problems of the…