Global sovability for the degenerate Krichhoff equation with real anlytic data.
Global stability of travelling fronts for a damped wave equation with bistable nonlinearity
We consider the damped wave equation on the whole real line, where is a bistable potential. This equation has travelling front solutions of the form which describe a moving interface between two different steady states of the system, one of which being the global minimum of . We show that, if the initial data are sufficiently close to the profile of a front for large , the solution of the damped wave equation converges uniformly on to a travelling front as . The proof of this global stability...
Global Strichartz estimates for variable coefficient second order hyperbolic operators
Global time estimates for solutions to equations of dissipative type
Global time estimates of norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.
Global uniqueness results for fractional order partial hyperbolic functional differential equations.
Global weak solutions for dimensional wave maps into homogeneous spaces
Global weak solutions of the wave map system to compact homogeneous spaces.
Global well-posedness and energy decay for a one dimensional porous-elastic system subject to a neutral delay
We consider a one-dimensional porous-elastic system with porous-viscosity and a distributed delay of neutral type. First, we prove the global existence and uniqueness of the solution by using the Faedo-Galerkin approximations along with some energy estimates. Then, based on the energy method with some appropriate assumptions on the kernel of neutral delay term, we construct a suitable Lyapunov functional and we prove that, despite of the destructive nature of delays in general, the damping mechanism...
Global well-posedness for two-dimensional semilinear wave equations.
Globally regular solutions to the Klein-Gordon equation
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...
Goursat and Darboux type problems for linear hyperbolic partial differential equations and systems.
Green's formula for right invertible operators
Green’s function pointwise estimates for the modified Lax–Friedrichs scheme
The aim of this paper is to find estimates of the Green’s function of stationary discrete shock profiles and discrete boundary layers of the modified Lax–Friedrichs numerical scheme, by using techniques developed by Zumbrun and Howard [27] in the continuous viscous setting.
Green's function pointwise estimates for the modified Lax–Friedrichs scheme
The aim of this paper is to find estimates of the Green's function of stationary discrete shock profiles and discrete boundary layers of the modified Lax–Friedrichs numerical scheme, by using techniques developed by Zumbrun and Howard [CITE] in the continuous viscous setting.
Group-theoretical solutions to gas dynamic equations generated by three-dimensional Lie subalgebras.
Hamilton-Jacobi functional differential equations with unbounded delay
The Cauchy problem for nonlinear functional differential equations on the Haar pyramid is considered. The phase space for generalized solutions is constructed. An existence theorem is proved by using the method of successive approximations. The theory of characteristics and integral inequalities are used. Examples of phase spaces are given.
Harmonic averages, exact difference schemes and local Green’s functions in variable coefficient PDE problems
A brief survey is given to show that harmonic averages enter in a natural way in the numerical solution of various variable coefficient problems, such as in elliptic and transport equations, also of singular perturbation types. Local Green’s functions used as test functions in the Petrov-Galerkin finite element method combined with harmonic averages can be very efficient and are related to exact difference schemes.
Hidden regularity for semilinear hyperbolic partial differential equations
High order accurate two-step approximations for hyperbolic equations