相关论文: Finite vs infinite derivative loss for abstract wa…
We investigate the initial value problem for some energy supercritical semilinear wave equations. We establish local existence in suitable spaces with continuous flow. We also obtain some ill-posedness/weak ill-posedness results. The proof…
In this paper, the existence, uniqueness and dependence on initial value of solution for a singular diffusion equation with nonlinear boundary condition are discussed. It is proved that there exists a unique global smooth solution which…
This paper is concerned with the existence of positive solutions of second-order impulsive differential equations with integral boundary conditions on an infinite interval. As an application, an example is given to demonstrate our main…
We consider a tsunami wave equation with singular coefficients and prove that it has a very weak solution. Moreover, we show the uniqueness results and consistency theorem of the very weak solution with the classical one in some appropriate…
We consider the initial value problem for the semilinear wave equation with time-dependent effective damping. The interest is the behavior of lifespan of solutions in view of the asymptotic profile of the damping as $t\to \infty$. The…
A general dispersion-dissipation condition for finite difference schemes is derived by analyzing the numerical dispersion and dissipation of explicit finite-difference schemes. The proper dissipation required to damp spurious…
We prove the existence and uniqueness, for wave speeds sufficiently large, of monotone traveling wave solutions connecting stable to unstable spatial equilibria for a class of $N$-dimensional lattice differential equations with…
The goal of this work is to determine classes of travelling solitary wave solutions for a differential approximation of a finite difference scheme by means of a hyperbolic ansatz. It is shown that spurious solitary waves can occur in…
In this work we study partial differential equations defined in a domain that moves in time according to the flow of a given ordinary differential equation, starting out of a given initial domain. We first derive a formulation for a…
In this paper, the discretization of a nonlinear wave equation whose nonlinear term is a power function is introduced. The difference equation derived by discretizing the nonlinear wave equation has solutions which show characteristics…
Discrete approximations to the equation \begin{equation*} L_{cont}u = u^{(4)} + D(x) u^{(3)} + A(x) u^{(2)} + (A'(x)+H(x)) u^{(1)} + B(x) u = f, \; x\in[0,1] \end{equation*} are considered. This is an extension of the Sturm-Liouville case…
This paper is concerned with the well-posedness of a time-fractional shallow-water equations, which has received little attention. In the realm of fractional calculus, numerous types of fractional derivatives have been explored in the…
In our previous two works, we studied the blow-up and lifespan estimates for damped wave equations with a power nonlinearity of the solution or its derivative, with scattering damping independently. In this work, we are devoted to…
We develop a fully discrete scheme for time-fractional diffusion equations by using a finite difference method in time and a finite element method in space. The fractional derivatives are used in Caputo sense. Stability and error estimates…
The aim of this paper is to study the finite space blow up of the solutions for a class of fourth order differential equations. Our results answer a conjecture in [F. Gazzola and R. Pavani. Wide oscillation finite time blow up for solutions…
Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and…
In this paper, we study the asymptotic behavior of solutions to the wave equation with damping depending on the space variable and growing at the spatial infinity. We prove that the solution is approximated by that of the corresponding heat…
We study propagation effects due to the finite speed of light in ionization of extended systems. We present a general quantitative theory of these effects and show under which conditions such effects should appear. The finite speed of light…
Spiral waves are a ubiquitous feature of the nonequilibrium dynamics of a great variety of excitable systems. In the limit of a large separation in timescale between fast excitation and slow recovery, one can reduce the spiral problem to…
In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the…