This paper establishes the equivalence between systems described by a single first-order hyperbolic partial differential equation and systems described by integral delay equations. Systemtheoretic results are provided for both classes of systems (among them converse Lyapunov results). The proposed framework can allow the study of discontinuous solutions for nonlinear systems described by a sing...

Hot deformation behavior of the Cu-Cr-Zr-Nd alloy was studied by hot compressive tests in the temperature range of 650-950 °C and the strain rate range of 0.001-10 s(-1) using Gleeble-1500D thermo-mechanical simulator. The results showed that the flow stress is strongly dependent on the deformation temperature and the strain rate. With the increase of temperature or the decrease of strain rate,...

git u) = c(8ft(ii), ? = x dt, where c(£) is a piecewise continuous function and h(u) is a smooth positive function whose first derivative does not change signs. The external effect is assumed to be finite; for simplicity, we suppose also that c(£) has compact support. Our main interest is the behavior of nonlinear waves when the resonance occurs, that is, when the characteristic speed f(u) is c...

We are interested in the large-time behavior of periodic entropy solutions in L to anisotropic degenerate parabolic-hyperbolic equations of second-order. Unlike the pure hyperbolic case, the nonlinear equation is no longer self-similar invariant and the diffusion term in the equation significantly affects the large-time behavior of solutions; thus the approach developed earlier based on the sel...

We generalize the approach first proposed by Manton [Nucl. Phys. B 150, 397 (1979)] to compute solitary wave interactions in translationally invariant, dispersive equations that support such localized solutions. The approach is illustrated using as examples solitons in the Korteweg-de Vries equation, standing waves in the nonlinear Schrödinger equation, and kinks as well as breathers of the sin...

Models of self-organizing bacterial communities and comparisons with experimental observations. dynamics with size dependency–strain phenomena. [4] Benoˆıt Perthame. Why hyperbolic and kinetic models for cell populations self-organization? In Hyperbolic problems: theory, numerics and applications , volume 67 of Proc. The non-local Fisher-KPP equation: travelling waves and steady states. [8] Phi...

We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism ...

We develop an analytical tool which is adept for detecting shapes of oscillatory functions, is useful in decomposing homogenization problems into limit-problems for kinetic equations. and provides an efficient framework for the validation of multi-scale asymptotic expansions. We apply it first to a hyperbolic homogenization problem and transform it to a hyperbolic limit problem for a kinetic eq...

In the method presented here, the discrete sine method, the basis functions consist of sine functions defined on a set of parallel discretization lines. The method is a combination of a scalar version of the finite difference method and the sine method. The choice of the basis set leads, for the eigenvalue equation to be solved, to a sparse matrix with a small bandwidth. As a consequence, the p...

In this paper, we established traveling wave solutions of the nonlinear evolution equation. The sine-cosine method was used to construct travelling wave solutions of the Fitzhugh-Nagumo equation and Cahn-Allen equation. Graphical interpretation shows that obtained results include periodic and Soliton wave solutions. It is also shown that for α =−1, solutions of Fitzhugh-Nagumo equation coincide...