Bifurcations near a double eigenvalue of the rectangular plate problem with a domain parametr
Blowup and asymptotic stability of weak solutions to wave equations with nonlinear degenerate damping and source terms.
Blow-up of solutions for an integro-differential equation with a nonlinear source.
Blowup of solutions of a nonlinear wave equation.
Blow-up of weak solutions for the semilinear wave equations with nonlinear boundary and interior sources and damping
We focus on the blow-up in finite time of weak solutions to the wave equation with interior and boundary nonlinear sources and dissipations. Our central interest is the relationship of the sources and damping terms to the behavior of solutions. We prove that under specific conditions relating the sources and the dissipations (namely p > m and k > m), weak solutions blow up in finite time.
Blow-up time of some nonlinear wave equations.
Boundary sentinels in cylindrical domains.
We study a model describing vibrations of a cylindrical domain with thickness e > 0. A characteristic of this model is that it contains pollution terms in the boundary data and missing terms in the initial data. The method of sentinels'' of J. L. Lions [7] is followed to construct a sentinel using the observed vibrations on the boundary. Such a sentinel, by construction, provides information on pollution terms independent of missing terms. This requires resolution of initial-boundary value...
Boundary value problems in time for wave equations on .
Bounded solutions of second order semicoercive evolution equations in a Hilbert space and of nonlinear telegraph equations.
Breakdown in finite time of solutions to a one-dimensional wave equation.
We consider a special type of a one-dimensional quasilinear wave equation wtt - phi (wt / wx) wxx = 0 in a bounded domain with Dirichlet boundary conditions and show that classical solutions blow up in finite time even for small initial data in some norm.