Initial-boundary value problem in nonlinear hyperbolic thermoelasticity. Some applications in continuum mechanics

Initial-Boundary Value Problem for Hyperbolic Equations

where Ji = 0 for x0 < 0. The problem is to find necessary and sufficient conditions on B(x, B) such that the initial-boundary value problem (1), (2), (3) is well-posed. Note that all theorems that a;re formulated below will also apply to the case when (1) is a general hyperbolic equation or a hyperbolic system of equations of arbitrary order provided that all components of the characteristic co...

The Initial Value Problem for Some Hyperbolic-dispersive System

We consider the initial value problem for some nonlinear hyperbolic and dispersive systems in one space dimension. Combining the classical energy method and the smoothing estimates for the Airy equation, we guarantee the time local well-posedness for this system. We also discuss the extension of our results to more general hyperbolic-dispersive system.

Lp-REGULARITY OF SOLUTIONS TO FIRST INITIAL-BOUNDARY VALUE PROBLEM FOR HYPERBOLIC EQUATIONS IN CUSP DOMAINS

In this article, we establish well-posedness and Lp-regularity of solutions to the first initial-boundary value problem for general higher order hyperbolic equations in cylinders whose base is a cusp domain.

Parametrix for a hyperbolic initial value problem with dissipation in some region

We construct parametrices for initial value problems of the form (∂z − iA(z,x,Dx) +B(z,x,Dx))u = 0, z > z0, u(z0, ·) = u0, (*) where (z,x) ∈ R × R, A(z,x,Dx) is a family of order 1 pseudodifferential operators with homogeneous real principal symbol a(z,x, ξ), and B(z,x,Dx) is a family of order γ > 0 pseudodifferential operators with non-negative homogeneous real principal symbol b(z,x, ξ). The ...

A Boundary Value Problem in the Hyperbolic Space