This paper obtains solitary waves, shock waves and singular solitons alon with conservation laws of the Rosenau Kortewegde Vries regularized long wave (R-KdV-RLW) equation with power law nonlinearity that models the dynamics of shallow water waves. The ansatz approach and the semi-inverse variational principle are used to obtain these solutions. The constraint conditions for the existence of so...

subtle points in the semi-inverse method of nonlinear elasticity BY RICCARDO DE PASCALIS, MICHEL DESTRADE* AND GIUSEPPE SACCOMANDI Dipartimento di Matematica, and Sezione di Ingegneria Industriale, Dipartimento di Ingegneria dell’Innovazione, Università degli Studi di Lecce, 73100 Lecce, Italy Institut Jean Le Rond d’Alembert, CNRS (UMR7190), Université Pierre et Marie Curie, Case 162, 4 Place ...

1 Linear algebra 2 1.1 Inner product, norm, distance, and orthogonality . . . . . . . . . 2 1.2 Angle and inequality . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Vector projection . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Basics of matrices . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5 Matrix multiplication . . . . . . . . . . . . . . . . . . . . . . . ....

Using uniform global Carleman estimates for semi-discrete elliptic and hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation, discretized by finite differences in a 2-d uniform mesh, from boundary or internal measurements. The discrete stability results, when compared with their continuous counterpar...

We consider the recovery of a potential associated with semi-linear wave equation on R n + 1 , ? . show that an unknown ( x t ) ? u m = 0 can be recovered in Hölder stable way from map | ? ? × [ T ] ? ? ? ? ? L 2 This data is equivalent to inner product Dirichlet-to-Neumann measurement function also prove similar stability result for when there noise added boundary data. The method we use const...

Using uniform global Carleman estimates for semi-discrete elliptic and hyperbolic equations, we study Lipschitz and logarithmic stability for the inverse problem of recovering a potential in a semi-discrete wave equation, discretized by finite differences in a 2-d uniform mesh, from boundary or internal measurements. The discrete stability results, when compared with their continuous counterpar...