Related papers: Optimal time-decay estimates for a diffusive Oldro…
We develop a convergence theory of space-time discretizations for the linear, 2nd-order wave equation in polygonal domains $\Omega\subset\mathbb{R}^2$, possibly occupied by piecewise homogeneous media with different propagation speeds.…
In this paper, we prove the global existence of analytical solutions to the compressible Oldroyd-B model without retardation near a non-vacuum equilibrium in ${\mathbb R}^n$ $(n=2,3)$. Zero retardation results in zero dissipation in the…
We prove optimal pointwise Schauder estimates in the spatial variables for solutions of linear parabolic integro-differential equations. Optimal H\"older estimates in space-time for those spatial derivatives are also obtained.
We introduce in this paper the numerical analysis of high order both in time and space Lagrange-Galerkin methods for the conservative formulation of the advection-diffusion equation. As time discretization scheme we consider the Backward…
Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-order time derivatives and a constant time-delay in the…
The global existence issue for the isentropic compressible Navier-Stokes equations in the critical regularity framework has been addressed in [7] more than fifteen years ago. However, whether (optimal) time-decay rates could be shown in…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
This paper establishes the optimal decay rate for scalar oscillatory integrals in $n$ variables which satisfy a nondegeneracy condition on the third derivatives. The estimates proved are stable under small linear perturbations, as…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
In this work, new finite difference schemes are presented for dealing with the upper-convected time derivative in the context of the generalized Lie derivative. The upper-convected time derivative, which is usually encountered in the…
In this paper, we consider the global regularity and the optimal time decay rate for the 2D isentropic hypo-viscous compressible Navier-Stokes equations. Firstly, we prove that there exists a global strong solution with the small initial…
When applying the finite-differences method to numerically solve the one-dimensional diffusion equation, one must choose discretization steps $\Delta x$, $\Delta t$ in space and time, respectively. By applying large-deviation theory on the…
The nonlocality of the fractional operator causes numerical difficulties for long time computation of the time-fractional evolution equations. This paper develops a high-order fast time-stepping discontinuous Galerkin finite element method…
We consider the Cauchy problem ($\mathbb{R}^d, d=2,3$) and the initial boundary values problem ($\mathbb{T}^d, d=2,3$)associated to the compressible Oldroyd-B model which is first derived by Barrett, Lu and S\"{u}li [Existence of large-data…
Exponential time differencing methods is a power tool for high-performance numerical simulation of computationally challenging problems in condensed matter physics, fluid dynamics, chemical and biological physics, where mathematical models…
Fractional partial differential equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we propose a local discontinuous Galerkin (LDG) method for the distributed-order time and…
This paper investigates the initial-boundary value problem for weakly coupled systems of time-fractional subdiffusion equations with spatially and temporally varying coupling coefficients. By combining the energy method with the coercivity…
We consider the initial value problem for cubic derivative nonlinear Schr\"odinger equations possessing weakly dissipative structure in one space dimension. We show that the small data solution decays like $O((\log t)^{-1/4})$ in $L^2$ as…
A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best…
We study the initial value problem associated to a higher dimensional version of the Benjamin-Ono equation. Our purpose is to establish local well-posedness results in weighted Sobolev spaces and to determinate according to them some sharp…