-convergence and homogenization of monotone damped hyperbolic equations.
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
We propose a numerical analysis of proper orthogonal decomposition (POD) model reductions in which a priori error estimates are expressed in terms of the projection errors that are controlled in the construction of POD bases. These error estimates are derived for generic parabolic evolution PDEs, including with non-linear Lipschitz right-hand sides, and for wave-like equations. A specific projection continuity norm appears in the estimates and – whereas a general uniform continuity bound seems out...
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
We propose a numerical analysis of proper orthogonal decomposition (POD) model reductions in which a priori error estimates are expressed in terms of the projection errors that are controlled in the construction of POD bases. These error estimates are derived for generic parabolic evolution PDEs, including with non-linear Lipschitz right-hand sides, and for wave-like equations. A specific projection continuity norm appears in the estimates and – whereas a general uniform continuity bound seems out...
Galerkin approximation with proper orthogonal decomposition : new error estimates and illustrative examples
We propose a numerical analysis of proper orthogonal decomposition (POD) model reductions in which a priori error estimates are expressed in terms of the projection errors that are controlled in the construction of POD bases. These error estimates are derived for generic parabolic evolution PDEs, including with non-linear Lipschitz right-hand sides, and for wave-like equations. A specific projection continuity norm appears in the estimates and – whereas a general uniform continuity bound seems out...
Gasdynamic regularity: some classifying geometrical remarks.
Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation
Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.
Gehring theory for time-discrete hyperbolic differential equations
This paper is concerned with extending Gehring theory to be applicable to Rothe's approximate solutions to hyperbolic differential equations.
Generalized characteristics uniqueness and regularity of solutions in a hyperbolic system of conservation laws
Generalized Function Algebras and PDEs with Singularities. A Survey.
Generalized Gevrey classes and multi-quasi-hyperbolic operators.
Generalized method of lines for first order partial functional differential equations
Classical solutions of initial boundary value problems are approximated by solutions of associated differential difference problems. A method of lines for an unknown function for the original problem and for its partial derivatives with respect to spatial variables is constructed. A complete convergence analysis for the method is given. A stability result is proved by using differential inequalities with nonlinear estimates of the Perron type for the given operators. A discretization...
Generalized n-dimensional Gronwall's inequality and its applications to non-selfadjoint and non-linear hyperbolic equations
Generalized periodic solutions of nonlinear telegraph equations (Preliminary communication)
Generalized Solution to a Semilinear Hyperbolic System with a Non-Lipshitz Nonlinearity.
Generalized solutions describing singularity interaction.
Generalized solutions of mixed problems for quasilinear hyperbolic systems of functional partial differential equations in the Schauder canonic form
Generalized solutions to boundary value problems for quasilinear hyperbolic systems of partial differential-functional equations
Generalized solutions to quasilinear hyperbolic systems in the second canonical form are investigated. A theorem on existence, uniqueness and continuous dependence upon the boundary data is given. The proof is based on the methods due to L. Cesari and P. Bassanini for systems which are not functional.
Generalized Solutions to Semilinear Hyperbolic Systems.
Generalized solutions to singular initial-boundary hyperbolic problems with non-lipshitz nonlinearities
Generalized Stability of Difference Method for Nonlinear Initial Value Problems and its Application