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 uses the finite speed of propagation and a quantitative study of the associated ODE. It does not require any scaling invariance of the equation.

In this paper, we are interested in the phenomenon of blow up in finite time (or formation of singularity in finite time) of solutions of the critical generalized KdV equation. Few results are known in the context of partial differential equations with a Hamiltonian structure. For the semilinear wave equation, or more generally for hyperbolic systems, the finite speed of propagation allows one ...

In this paper, a new algorithm for studying elastic wave propagation in the phononic crystals is presented. At first, the displacement-based forms of elastic wave equations are derived and then the forms are discretized using finite difference method. So the new algorithm is called the displacement-based finite difference time domain (DBFDTD). Three numerical examples are computed with this met...

A 2D finite element model for the solution of wave equations is developed. The fluid is considered as incompressible and irrotational. This is a difficult mathematical problem to solve numerically as well as analytically because the condition of the dynamic boundary (Bernoulli’s equation) on the free surface is not fixed and varies with time. The finite element technique is applied to solve non...

We consider an abstract wave equation with a propagation speed that depends only on time. investigate well-posedness results finite derivative loss in the case where is smooth for positive times, but potentially singular at initial prove solutions exhibit under family of conditions involve blow up rate first and second speed, spirit weaker requirement derivative, stronger derivative. Our interp...

The effects of wave direction, frequency and the waterline shape of floating structures on the wave mean drift force formula have been considered separately by several authors but there isn't a general formula to take into account all of these effects. In this regard, Faltinsen’s wave drift force formula has been modified by adding finite draft coefficient. The results obtained from this formu...

Left ventricular (LV) wave speed (LVWS) was studied experimentally and confirmed in theory. Combining the definition of elastance (E) with the equations for the conservation of mass and momentum shows that LVWS is proportional to the square root of ELA, where L is long-axis length and A is the cross-sectional area, and the density of the blood. (We defined ELA = gamma, where gamma is compressib...

metal spinning as a kind of manufacturing process has capability to shape hollow components. in present work shear spinning process is used to formplates into conical shapes. moreover, the aim of this research is to demonstrate the impact of the process parameters (i.e. feeding rate and spindle speed) on wall thickness. this approachwas done by experimental and finite elements method. the resul...

The inverse scattering problem on the line is studied for the generalized Schrodinger equation (d* f/V&*) + @H(X)* fi= Q(X) $, where H(x) is a positive, piecewise continuous function with positive limits H, as x --+ 2~. This equation, in the frequency domain, describes the wave propagation in a nonhomogeneous medium, where Q(X) is the restoring force and l/H(x) is the variable wave speed changi...