Related papers: On the zero-dispersion limit of the Benjamin-Ono C…
We consider the Cauchy problem on a nonlinear conversation law with large initial data. By Green's function methods, energy methods, Fourier analysis, frequency decomposition, pseudo-differential operators, we obtain the global existence…
In this paper, a boundary value problem for a singularly perturbed linear system of two second order ordinary differential equations of convection- diffusion type is considered on the interval [0, 1]. The components of the solution of this…
We consider a wave equation with a nonlocal logarithmic damping depending on a small parameter $\theta \in (0,1/2)$. This research is a counter part of that was initiated by Charao-D'Abbicco-Ikehata considered in [5] for the large parameter…
We consider the Cauchy problem associated to the fourth-order nonlinear Schr\"{o}dinger-Hartree equation with variable dispersion coefficients. The variable dispersion coefficients are assumed to be continuous or periodic and piecewise…
We investigate the qualitative behavior of the initial traces of nonnegative solutions to the fast diffusion equation with power-type nonlinearity. Necessary conditions for the existence of solutions to the corresponding Cauchy problem are…
We consider the Cauchy problem for the two-dimensional Novikov-Veselov equation integrable via the inverse scattering problem for the Schr\"odinger operator with fixed negative energy. The associated linear equation is characterized by a…
We study the existence and qualitative properties of solutions to the Cauchy problem associated to the quasilinear reaction-diffusion equation $$ \partial_tu=\Delta u^m+(1+|x|)^{\sigma}u^p, $$ posed for $(x,t)\in\real^N\times(0,\infty)$,…
We study the asymptotic behaviour of positive solutions of the Cauchy problem for the fast diffusion equation near the extinction time. We find a continuum of rates of convergence to a self-similar profile. These rates depend explicitly on…
In this paper, we investigate the Cauchy problem for the Ostrovsky equation \begin{eqnarray*} \partial_{x}\left(u_{t}-\beta \partial_{x}^{3}u +\frac{1}{2}\partial_{x}(u^{2})\right) -\gamma u=0, \end{eqnarray*} in the Sobolev space…
In this paper, we investigate the well-posedness and the long-time asymptotic behavior for the initial-boundary value problem for multi-term time-fractional diffusion equations, where the time differentiation consists of a finite summation…
We study the Cauchy problem in $n$-dimensional space for the system of Navier-Stokes equations in critical mixed-norm Lebesgue spaces. Local well-posedness and global well-posedness of solutions are established in the class of critical…
In this paper, we consider the low Mach and Rossby number singular limits and longtime existence of strong solution to the initial value problem of 3D compressible rotating Euler equations with ill-prepared initial data. We establish the…
This paper is devoted to the Cauchy problem for the stochastic generalized Benjamin-Ono equation. By using the Bourgain spaces and Fourier restriction method and the assumption that $u_{0}$ is $\mathcal{F}_{0}$-measurable, we prove that the…
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathematical modeling of ultra-slow diffusion processes observed in…
The Cauchy problem for the Korteweg de Vries (KdV) equation with small dispersion of order $\epsilon^2$, is characterized by the appearance of a zone of rapid modulated oscillations of wave-length of order $\epsilon$. These oscillations are…
We compute the scattering data of the Benjamin-Ono equation for arbitrary rational initial conditions with simple poles. Specifically, we obtain explicit formulas for the Jost solutions and eigenfunctions of the associated spectral problem,…
The initial-boundary value problem (ibvp) for the $m$-th order dispersion Korteweg-de Vries (KdV) equation on the half-line with rough data and solution in restricted Bourgain spaces is studied using the Fokas Unified Transform Method…
I examine some analytical properties of a nonlinear reaction-diffusion system that has been used to model the propagation of a wildfire. I establish global-in-time existence and uniqueness of bounded mild solutions to the Cauchy problem for…
We consider the Cauchy problem for the spatially inhomogeneous Landau equation with soft potentials in the case of large (i.e. non-perturbative) initial data. We construct a solution for any bounded, measurable initial data with uniform…
We consider the initial-boundary value problem for an incompressible Oldroyd-B model with stress diffusion in two-dimensional upper half plane which describes the motion of viscoelastic polymeric fluids. From the physical point of view, the…