Dirichlet and Neumann problems for string equation, Poncelet problem and Pell-Abel equation.
Dirichlet problem for a nonlinear conservation law.
In this paper we propose the study of a first-order non-linear hyperbolic equation in a bounded domain. We give a result of existence and uniqueness of the entropic measure-valued solution and of the entropic weak solution; for some general assumptions on the data.
Discontinous Solutions of a Nonlinear Hyperbolic Equation with Unilateral Constraints.
Discontinuous solutions of the Cauchy problems for a scalar equation in nonconservative form
Discontinuous travelling wave solutions for a class of dissipative hyperbolic models
Discontinuous shock structure solutions for a general system of balance laws is considered in order to investigate the problem of connecting two equilibrium states lying on different sides of a singular barrier representing a locus of irregular singular points for travelling waves. Within such a theoretical setting a governing system of monoatomic gas is considered.
Discontinuous wave equations and a topological degree for some classes of multi-valued mappings
The Leray-Schauder degree is extended to certain multi-valued mappings on separable Hilbert spaces with applications to the existence of weak periodic solutions of discontinuous semilinear wave equations with fixed ends.
Dispersive and Strichartz estimates for the wave equation in domains with boundary
In this note we consider a strictly convex domain of dimension with smooth boundary and we describe the dispersive and Strichartz estimates for the wave equation with the Dirichlet boundary condition. We obtain counterexamples to the optimal Strichartz estimates of the flat case; we also discuss the some results concerning the dispersive estimates.
Dispersive estimates for a linear wave equation with electromagnetic potential.
Dispersive Estimates of Solutions to the Wave Equation with a Potential in Dimensions Two and Three
2000 Mathematics Subject Classification: 35L15, 35B40, 47F05.We prove dispersive estimates for solutions to the wave equation with a real-valued potential V.
Dispersive limits in the homogenization of the wave equation
Dispersive waves and caustics.
Distribution near the real axis of scattering poles generated by a non-hyperbolic periodic ray
Distributional derivatives of functions of two variables of finite variation and their application to an impulsive hyperbolic equation
We give characterizations of the distributional derivatives , , of functions of two variables of locally finite variation. Then we use these results to prove the existence theorem for the hyperbolic equation with a nonhomogeneous term containing the distributional derivative determined by an additive function of an interval of finite variation. An application of the above theorem to a hyperbolic equation with an impulse effect is also given.
Distributions and heat equation in
Divergence boundary conditions for vector Helmholtz equations with divergence constraints
The idea of replacing a divergence constraint by a divergence boundary condition is investigated. The connections between the formulations are considered in detail. It is shown that the most common methods of using divergence boundary conditions do not always work properly. Necessary and sufficient conditions for the equivalence of the formulations are given.
Dual dynamic approach to shape optimization