Related papers: Fourth-order dispersive systems on the one-dimensi…
This paper is concerned with the initial value problem for a system of one-dimensional fourth-order dispersive partial differential equations on the torus with nonlinearity involving derivatives up to second order. This paper gives…
A fourth-order dispersive flow equation for closed curves on the canonical two-dimensional unit sphere arises in some contexts in physics and fluid mechanics. In this paper, a geometric generalization of the sphere-valued model is…
We present the necessary and sufficient condition for the $L^2$-well-posedness of the initial problem for a third order linear dispersive equation on the two dimensional torus. Birkhoff's method of asymptotic solutions is used to prove the…
We discuss a short-time existence theorem of solutions to the initial value problem for a fourth-order dispersive flow for curves parametrized by the real line into a compact K\"ahler manifold. Our equations geometrically generalize a…
This paper investigates the initial value problem for a system of one-dimensional fourth-order dispersive partial differential-integral equations with nonlinearity involving derivatives up to second order. Examples of the system arise in…
We study families of smooth immersed regular planar curves $ \alpha : \left [-1,1 \right ]\times \left [0,T \right )\to \mathbb{R}^{2}$ satisfying the fourth order nonlinear curve diffusion flow with generalised Neumann boundary conditions…
This paper is concerned with a fourth order nonlinear dispersive partial differential equation for closed curve flow on a K\"ahler manifold. The main results is that the initial value problem has a solution locally in time if the K\"ahler…
An initial-boundary value problem for a time-fractional subdiffusion equation with the Riemann-Liouville derivatives on N-dimensional torus is considered. The uniqueness and existence of the classical solution of the posed problem are…
We study the well-posedness of the initial value problem on periodic intervals for linear and quasilinear evolution equations for which the leading-order terms have three spatial derivatives. In such equations, there is a competition…
A new solution to the mono-dimensional diffusion equation for time-variable first kind boundary condition is presented where the time-variable function at the surface is derived proposing a surface saturation model. This solution may be…
We prove the unconditional well-posedness for the fourth order nonlinear Schrodinger type equations in H^s(\mathbb{T}) when s \geq 1, which includes the non-integrable case. This regularity threshold is optimal because the nonlinear terms…
We regard the Cauchy problem for a particular Whitham-Boussinesq system modelling surface waves of an inviscid incompressible fluid layer. We are interested in well-posedness at a very low level of regularity. We derive dispersive and…
We consider closed immersed hypersurfaces in $\R^{3}$ and $\R^4$ evolving by a class of constrained surface diffusion flows. Our result, similar to earlier results for the Willmore flow, gives both a positive lower bound on the time for…
A fourth-order compact scheme is proposed for a fourth-order subdiffusion equation with the first Dirichlet boundary conditions. The fourth-order problem is firstly reduced into a couple of spatially second-order system and we use an…
We consider a fourth-order regularization of the curvature flow for an immersed plane curve with fixed boundary, using an elastica-type functional depending on a small positive parameter $\varepsilon$. We show that the approximating flow…
This paper focuses on a one-dimensional fourth-order nonlinear dispersive partial differential equation for curve flows on a K\"ahler manifold. The equation arises as a fourth-order extension of the one-dimensional Schr\"odinger flow…
This paper is devoted to studying the initial value problem for a third-order dispersive equation for closed curves into K\"ahler manifolds. This equation is a geometric generalization of a two-sphere valued system modeling the motion of…
We study dispersive models of fluid flow in viscoelastic vessels, derived in the study of blood flow. The unknowns in the models are the velocity of the fluid in the axial direction and the displacement of the vessel wall from rest. We…
We prove global existence of solutions to the initial value problem for a third order dispersive flow into compact locally Hermitian symmetric spaces. The equation we consider generalizes two-sphere-valued completely integrable systems…
We study a basic plasma physics model--the one-fluid Euler--Poisson system on the square torus, in which a compressible electron fluid flows under its own electrostatic field. In this paper we prove long-term regularity of periodic…