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
Generalized Strichartz Inequalities for the Wave Equation on the Laguerre Hypergroup
Mathematics Subject Classification: 42B35, 35L35, 35K35In this paper we study generalized Strichartz inequalities for the wave equation on the Laguerre hypergroup using generalized homogeneous Besov-Laguerre type spaces.
Generators of hyperbolic heat equation in nonlinear thermoelasticity
Generic properties of generalized hyperbolic partial differential equations
The existence and uniqueness of solutions and convergence of successive approximations are considered as generic properties for generalized hyperbolic partial differential equations with unbounded right-hand sides.
Genuinely multi-dimensional non-dissipative finite-volume schemes for transport
We develop a new multidimensional finite-volume algorithm for transport equations. This algorithm is both stable and non-dissipative. It is based on a reconstruction of the discrete solution inside each cell at every time step. The proposed reconstruction, which is genuinely multidimensional, allows recovering sharp profiles in both the direction of the transport velocity and the transverse direction. It constitutes an extension of the one-dimensional reconstructions analyzed in (Lagoutière, 2005;...
Geometric optics expansions with amplification for hyperbolic boundary value problems: Linear problems
We compute and justify rigorous geometric optics expansions for linear hyperbolic boundary value problems that do not satisfy the uniform Lopatinskii condition. We exhibit an amplification phenomenon for the reflection of small high frequency oscillations at the boundary. Our analysis has two important consequences for such hyperbolic boundary value problems. Firstly, we make precise the optimal energy estimate in Sobolev spaces showing that losses of derivatives must occur from the source terms...
Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems.
Geometric renormalization of large energy wave maps
There has been much progress in recent years in understanding the existence problem for wave maps with small critical Sobolev norm (in particular for two-dimensional wave maps with small energy); a key aspect in that theory has been a renormalization procedure (either a geometric Coulomb gauge, or a microlocal gauge) which converts the nonlinear term into one closer to that of a semilinear wave equation. However, both of these renormalization procedures encounter difficulty if the energy of the...