111 research outputs found
Nonlinear Waves and Dispersive Equations
[no abstract available
Very Singular Similarity Solutions and Hermitian Spectral Theory for Semilinear Odd-Order PDEs
Very singular self-similar solutions of semilinear odd-order PDEs are studied
on the basis of a Hermitian-type spectral theory for linear rescaled odd-order
operators.Comment: 49 pages, 12 Figure
Carleman estimates for the Zaremba Boundary Condition and Stabilization of Waves
In this paper, we shall prove a Carleman estimate for the so-called Zaremba
problem. Using some techniques of interpolation and spectral estimates, we
deduce a result of stabilization for the wave equation by means of a linear
Neumann feedback on the boundary. This extends previous results from the
literature: indeed, our logarithmic decay result is obtained while the part
where the feedback is applied contacts the boundary zone driven by an
homogeneous Dirichlet condition. We also derive a controllability result for
the heat equation with the Zaremba boundary condition.Comment: 37 pages, 3 figures. Final version to be published in Amer. J. Mat
Finite element error analysis of wave equations with dynamic boundary conditions: estimates
norm error estimates of semi- and full discretisations, using
bulk--surface finite elements and Runge--Kutta methods, of wave equations with
dynamic boundary conditions are studied. The analysis resides on an abstract
formulation and error estimates, via energy techniques, within this abstract
setting. Four prototypical linear wave equations with dynamic boundary
conditions are analysed which fit into the abstract framework. For problems
with velocity terms, or with acoustic boundary conditions we prove surprising
results: for such problems the spatial convergence order is shown to be less
than two. These can also be observed in the presented numerical experiments
- …