The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations, coupled to one another along the moving material interface through the continuity of the velocity and traction vectors. We prove the existence and uniqueness (locally in time) of strong solutions in Sobolev spaces for quasilinear elastodynamics coupled to the incompressible...

The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations, coupled to one another along the moving material interface through the continuity of the velocity and traction vectors. We prove the existence and uniqueness (locally in time) of strong solutions in Sobolev spaces for quasilinear elastodynamics coupled to the incompressible...

The interaction of an oblique line soliton with a one-dimensional dynamic mean flow is analyzed using the Kadomtsev-Petviashvili II (KPII) equation. Building upon previous studies that examined transmission or trapping by slowly varying rarefaction oscillatory dispersive shock wave in one space and time dimension, this paper allows for incident to approach changing at nonzero angle. By deriving...

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...

This paper is concerned with the optimal control of a class of distributed systems described by first order, quasilinear hyperbolic partial differential equations. In particular, this paper investigates an optimal control problem of a flow recirculation system; namely, a closed-circuit wind tunnel. The flow recirculation is modeled by the Euler equations with boundary conditions prescribing flo...

In this paper the mechanism and the character of the formation of singularities caused by eigenvalues or (and) eigenvectors, respectively, will be discussed for 1-D quasilinear hyperbolic systems.

Our goal is to establish the theorems of existence and multiple of positive entire solutions for a class quasilinear elliptic equations in RN with the Schauder-Tychonoff fixed point theorem as the principal tool. In many articles, the theorems of existence and multiple of positive entire solutions for a class semilinear elliptic equations are established. The results of the semilinear equations...

Abstract In this paper, the mixed initial-boundary value problem for inhomogeneous quasilinear strictly hyperbolic systems with nonlinear boundary conditions in the first quadrant {(t, x)| t ≥ 0, x ≥ 0} is investigated. Under the assumption that the right hand side satisfies matching condition and the system is strictly hyperbolic and weakly linearly degenerate, we obtain the global existence a...