Generalized solutions to symmetric hyperbolic systems with discontinuous coefficients: The multidimensional case

Hyperbolic equations and systems with discontinuous coefficients or source terms

This paper is devoted to the study of some nonlinear hyperbolic equations or systems with discontinuous coefficients or with source terms. The common feature of the considered problems is the fact that the jacobian matrix of an associated autonomous system is not diagonalizable in R for many values of the unknown (leading to linear ill posed problems). However, the nonlinear problems appear to ...

Viscous approach for Linear Hyperbolic Systems with Discontinuous Coefficients

— We introduce small viscosity solutions of hyperbolic systems with discontinuous coefficients accross the fixed noncharacteristic hypersurface {xd = 0}. Under a geometric stability assumption, our first result is obtained, in the multi-D framework, for piecewise smooth coefficients. For our second result, the considered operator is ∂t+a(x)∂x, with sign(xa(x)) > 0 (expansive case not included i...

Exponential Decay of Weak Solutions for Hyperbolic Systems of First Order with Discontinuous Coefficients

Exact Solutions to a Generalized BBM Equation with Variable Coefficients

An auxiliary equation technique is applied to investigate a generalized Benjamin-Bona-Mahony equation with variable coefficients. Many exact traveling wave solutions are obtained which include algebraic solutions, solitons, solitary wave solutions and trigonometric solutions. Mathematics Subject Classification: 35Q53, 35B35

Viscosity Solutions of Hamilton–jacobi Equations with Discontinuous Coefficients

Abstract. We consider Hamilton–Jacobi equations, where the Hamiltonian depends discontinuously on both the spatial and temporal location. Our main results is the existence of viscosity solution to the Cauchy problem, and that the front tracking algorithm yields an L∞ contractive semigroup. We define a viscosity solution by treating the discontinuities in the coefficients analogously to “interna...