相关论文: The initial value problem for a third order disper…

We consider the initial value problem to the Isobe-Kakinuma model for water waves and the structure of the model. The Isobe-Kakinuma model is the Euler-Lagrange equations for an approximate Lagrangian which is derived from Luke's Lagrangian…

A bilinear estimate in terms of Bourgain spaces associated with a linearised Kadomtsev-Petviashvili-type equation on the three-dimensional torus is shown. As a consequence, time localized linear and bilinear space time estimates for this…

The purpose of this paper is to study well-posedness of the initial value problem (IVP) for the inhomogeneous nonlinear Schr\"odinger equation (INLS) $$ i u_t +\Delta u+\lambda|x|^{-b}|u|^\alpha u = 0, $$ where $\lambda=\pm 1$ and $\alpha$,…

We consider the initial value problem for a pseudodifferential equation with first order hyperbolic part, and an order $\gamma > 0$ dissipative term. Under an assumption, depending on an integer parameter $L \geq 2$ such that $2 \gamma <…

We investigate the local wellposedness of incompressible inhomogeneous Navier-Stokes equations on the Torus $\T^3$, with initial data in the critical Besov spaces. Under some smallness assumption on the velocity in the critical space…

A choice of first-order variables for the characteristic problem of the linearized Einstein equations is found which casts the system into manifestly well-posed form. The concept of well-posedness for characteristic problems invoked is that…

In this paper we focus on the initial value problem for quasi-linear dissipative plate equation in multi-dimensional space $(n\geq2)$. This equation verifies the decay property of the regularity-loss type, which causes the difficulty in…

The problem of obtaining necessary and sufficient conditions for local existence of non-negative solutions in Lebesgue spaces for semilinear heat equations having monotonically increasing source term $f$ has only recently been resolved…

We present an optimization problem in infinite dimensions which satisfies the usual second-order sufficient condition but for which perturbed problems fail to possess solutions.

We study the well-posedness of the initial value problem for fully nonlinear evolution equations, $u_{t}=f[u],$ where $f$ may depend on up to the first three spatial derivatives of $u.$ We make three primary assumptions about the form of…

We examine initial-boundary value problems for diffusion equations with distributed order time-fractional derivatives. We prove existence and uniqueness results for the weak solution to these systems, together with its continuous dependency…

This paper addresses the problem of finding an asymptotic solution for first and second order integro-differential equations containing an arbitrary kernel, by evaluating the corresponding inverse Laplace and Fourier transforms. The aim of…

By using the continuous induction method, we prove that the initial value problem of the three dimensional Navier-Stokes equations is globally well-posed in $L^p(\mathbb{R}^3)\cap L^2(\mathbb{R}^3)$ for any $3<p<\infty$. The proof is rather…

We consider the $L^2$ well-posedness of third order Benjamin-Ono equation. We show that by means of a normal form and a gauge transformation, the equation can be changed into an Airy-type equation. A second goal of this work is to establish…

In this paper we present a very simple proof of the existence of at least one non trivial solution for a Kirchhoff type equation on $\RN$, for $N\ge 3$. In particular, in the first part of the paper we are interested in studying the…

We improve results regarding the stability and attractivity of solutions $u$ of a large class of initial-boundary-value problems characterized by a semi-linear third order equation which may contain time-dependent coefficients. In the proof…

We consider the non linear wave equation (NLW) on the d-dimensional torus with a smooth nonlinearity of order at least two at the origin. We prove that, for almost any mass, small and smooth solutions of high Sobolev indices are stable up…

We investigate the observability of a general class of linear dispersive equations on the torus $\mathbb{T}$. We take one line segment or two line segments in space-time region as the observable set. We give the characteristic on the slopes…

We consider initial-boundary-value problems for a class of nonlinear third order equations having non-autonomous forcing terms and get new asymptotic stability results by means of the Liapunov second method. The class includes equations…

In this paper, we consider the almost sure well-posedness of the Cauchy problem to the Cahn-Hilliard-Navier-Stokes equation with a randomization initial data on a torus $\mathbb{T}^3$. First, we prove the local existence and uniqueness of…