A new approach for the analysis of Vortex Methods in two and three dimensions
A new approach to solve a nonlinear wave equation.
A new conservative difference scheme for the general Rosenau-RLW equation.
A new kind of the solution of degenerate parabolic equation with unbounded convection term
A new kind of entropy solution of Cauchy problem of the strong degenerate parabolic equation [...] is introduced. If u0 ∈ L∞(RN), E = {Ei} ∈ (L2(QT))N and divE ∈ L2(QT), by a modified regularization method and choosing the suitable test functions, the BV estimates are got, the existence of the entropy solution is obtained. At last, by Kruzkov bi-variables method, the stability of the solutions is obtained.
A new method to obtain decay rate estimates for dissipative systems
A new method to obtain decay rate estimates for dissipative systems with localized damping.
We consider the wave equation damped with a locally distributed nonlinear dissipation. We improve several earlier results of E. Zuazua and of M. Nakao in two directions: first, using the piecewise multiplier method introduced by K. Liu, we weaken the usual geometrical conditions on the localization of the damping. Then thanks to some new nonlinear integral inequalities, we eliminate the usual assumption on the polynomial growth of the feedback in zero and we show that the energy of the system decays...
A new method to obtain decay rate estimates for dissipative systems
We consider the wave equation damped with a boundary nonlinear velocity feedback p(u'). Under some geometrical conditions, we prove that the energy of the system decays to zero with an explicit decay rate estimate even if the function ρ has not a polynomial behavior in zero. This work extends some results of Nakao, Haraux, Zuazua and Komornik, who studied the case where the feedback has a polynomial behavior in zero and completes a result of Lasiecka and Tataru. The proof is based on the construction...
A new numerical model for propagation of tsunami waves
A new model for propagation of long waves including the coastal area is introduced. This model considers only the motion of the surface of the sea under the condition of preservation of mass and the sea floor is inserted into the model as an obstacle to the motion. Thus we obtain a constrained hyperbolic free-boundary problem which is then solved numerically by a minimizing method called the discrete Morse semi-flow. The results of the computation in 1D show the adequacy of the proposed model.
A new two-dimensional shallow water model including pressure effects and slow varying bottom topography
The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...
A new two-dimensional Shallow Water model including pressure effects and slow varying bottom topography
The motion of an incompressible fluid confined to a shallow basin with a slightly varying bottom topography is considered. Coriolis force, surface wind and pressure stresses, together with bottom and lateral friction stresses are taken into account. We introduce appropriate scalings into a three-dimensional anisotropic eddy viscosity model; after averaging on the vertical direction and considering some asymptotic assumptions, we obtain a two-dimensional model, which approximates the three-dimensional...
A nonexistence result for a nonlinear PDE with Robin condition.
A nonlinear boundary value problem for a system of hyperbolic partial differential equations.
A non-linear hyperbolic equation.
A nonlinear transmission problem with time dependent coefficients.
A nonlinear wave equation with a nonlinear integral equation involving the boundary value.
A nonlocal mixed semilinear problem for second-order hyperbolic equations.
A nonlocal problem for fourth order hyperbolic equations with multiple characteristics.
A non-local problem with integral conditions for hyperbolic equations.
A note on -point conservative monotone schemes
First–order accurate monotone conservative schemes have good convergence and stability properties, and thus play a very important role in designing modern high resolution shock-capturing schemes. Do the monotone difference approximations always give a good numerical solution in sense of monotonicity preservation or suppression of oscillations? This note will investigate this problem from a numerical point of view and show that a -point monotone scheme may give an oscillatory solution even though...
A note on (2K+1)-point conservative monotone schemes
First–order accurate monotone conservative schemes have good convergence and stability properties, and thus play a very important role in designing modern high resolution shock-capturing schemes. Do the monotone difference approximations always give a good numerical solution in sense of monotonicity preservation or suppression of oscillations? This note will investigate this problem from a numerical point of view and show that a (2K+1)-point monotone scheme may give an oscillatory solution even...