Gasdynamic regularity: some classifying geometrical remarks.
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 Semilinear Hyperbolic Systems.
Geometric optics with critical vanishing viscosity for one-dimensional semilinear initial value problems.
Global boundary controllability of the de St. Venant equations between steady states
Global classical solutions to a kind of mixed initial-boundary value problem for inhomogeneous quasilinear hyperbolic systems
In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant is investigated. Under the assumption that the right-hand side satisfies a matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence and uniqueness of a solution and its stability with certain small initial and boundary data.
Global Existence for Quasi-Linear Dissipative Wave Equations with Large Data and Small Parameter.
Global existence for the nonlinear equations of crystal optics
Global existence of solutions for the 1-D radiative and reactive viscous gas dynamics
In this paper, we prove the existence of a global solution to an initial-boundary value problem for 1-D flows of the viscous heat-conducting radiative and reactive gases. The key point here is that the growth exponent of heat conductivity is allowed to be any nonnegative constant; in particular, constant heat conductivity is allowed.
Global smooth solutions of some quasi-linear hyperbolic systems with large data
Global solution of mixed problem for a certain system of nonlinear conservation laws
Global solvability of the mixed problem for first order functional partial differential equations
Godunov method for nonconservative hyperbolic systems
This paper is concerned with the numerical approximation of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The theory developed by Dal Maso et al. [J. Math. Pures Appl.74 (1995) 483–548] is used in order to define the weak solutions of the system: an interpretation of the nonconservative products as Borel measures is given, based on the choice of a family of paths drawn in the phase space. Even if the family of paths can be chosen arbitrarily, it is natural to require this...
Group-theoretical solutions to gas dynamic equations generated by three-dimensional Lie subalgebras.