A note on a theorem of Jörgens.
A note on critical times of quasilinear hyperbolic systems
In this paper the exact formula for the critical time of generating discontinuity (shock wave) in a solution of a quasilinear hyperbolic system is derived. The applicability of the formula in the engineering praxis is shown on one-dimensional equations of isentropic non-viscous compressible fluid flow.
A note on hyperbolic partial differential equations. II.
A Note on Maximal Rate of Decay for Solutions to Some Linear Wave Equations.
A note on nontrivial periodic solutions of dynamical systems with subquadratic potential.
We obtain non-constant periodic solutions for a class of second-order autonomous dynamic systems whose potential is subquadratic at infinity. We give a theorem on conjugate points for convex potentials.
A note on poroacoustic traveling waves under Darcy's law: Exact solutions
A mathematical analysis of poroacoustic traveling wave phenomena is presented. Assuming that the fluid phase satisfies the perfect gas law and that the drag offered by the porous matrix is described by Darcy's law, exact traveling wave solutions (TWS)s, as well as asymptotic/approximate expressions, are derived and examined. In particular, stability issues are addressed, shock and acceleration waves are shown to arise, and special/limiting cases are noted. Lastly, connections to other fields are...
A Note on Shock Profiles in Dissipative Hyperbolic and Parabolic Models
A note on the difference schemes for hyperbolic equations.
A note on the uniqueness of entropy solutions to first order quasilinear equations.
A note on wave equation and convolutions.
A note to a bifurcation result of H. Kielhöfer for the wave equation
A modification of a classical number-theorem on Diophantine approximations is used for generalizing H. kielhöfer's result on bifurcations of nontrivial periodic solutions to nonlinear wave equations.
A parameter-free smoothness indicator for high-resolution finite element schemes
This paper presents a postprocessing technique for estimating the local regularity of numerical solutions in high-resolution finite element schemes. A derivative of degree p ≥ 0 is considered to be smooth if a discontinuous linear reconstruction does not create new maxima or minima. The intended use of this criterion is the identification of smooth cells in the context of p-adaptation or selective flux limiting. As a model problem, we consider a 2D convection equation discretized with bilinear finite...
A parametrix construction for wave equations with coefficients
In this article we give a construction of the wave group for variable coefficient, time dependent wave equations, under the hypothesis that the coefficients of the principal term possess two bounded derivatives in the spatial variables, and one bounded derivative in the time variable. We use this construction to establish the Strichartz and Pecher estimates for solutions to the Cauchy problem for such equations, in space dimensions and .
A Particle Method for First-order Symmetric Systems.
A positivity preserving central scheme for shallow water flows in channels with wet-dry states
We present a high-resolution, non-oscillatory semi-discrete central scheme for one-dimensional shallow-water flows along channels with non uniform cross sections of arbitrary shape and bottom topography. The proposed scheme extends existing central semi-discrete schemes for hyperbolic conservation laws and enjoys two properties crucial for the accurate simulation of shallow-water flows: it preserves the positivity of the water height, and it is well balanced, i.e., the source terms arising from...
A potential well theory for the wave equation with a nonlinear boundary condition.
A priori estimate for discontinuous solutions of a second order linear hyperbolic problem.
A priori estimates for higher order hyperbolic equations.
A priori estimates for solutions of spinodal decomposition problem.
A property of the defining equations for the Lie algebra in the group classification problem for wave equations.