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The thermal radiative transfer equations model temperature evolution through a background medium as a result of radiation. When a large number of particles are absorbed in a short time scale, the dynamics tend to a non-linear diffusion-type…
This report addresses the solution of Riemann problems for hyperbolic equations when the nonlinear characteristic fields loose their genuine nonlinearity. In this context, exact solvers for nonconvex 1D Riemann problems are developed. First…
These lectures present the analysis of stability and control of long time behavior of PDE models described by nonlinear evolutions of hyperbolic type. Specific examples of the models under consideration include: (i) nonlinear systems of…
We construct examples of oscillating solutions with persistent oscillations for various hyperbolic-parabolic systems with singular diffusion matrices that appear in mechanics. These include, an example for the equations of nonlinear…
We investigate the stability of the wave equation with spatial dependent coefficients on a bounded multidimensional domain. The system is stabilized via a scattering passive feedback law. We formulate the wave equation in a port-Hamiltonian…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytical solutions of the nonlinear field equations are…
We consider a periodic array of resonators, formed from Euler-Bernoulli beams, attached to the surface of an elastic half-space. Earlier studies of such systems have concentrated on compressional resonators. In this paper we consider the…
We are concerned with the problem of determining the nonlinear term in a semilinear elliptic equation by boundary measurements. Precisely, we improve [5, Theorem 1.3], where a logarithmic type stability estimate was proved. We show actually…
We provide a justification with rigorous error estimates showing that the leading term in weakly nonlinear geometric optics expansions of highly oscillatory reflecting pulses is close to the uniquely determined exact solution for small…
In this paper, both structural and dynamical stabilities of steady transonic shock solutions for one-dimensional Euler-Poission system are investigated. First, a steady transonic shock solution with supersonic backgroumd charge is shown to…
We develop a version of Haar and Holmgren methods which applies to discontinuous solutions of nonlinear hyperbolic systems and allows us to control the L1 distance between two entropy solutions. The main difficulty is to cope with linear…
We complete previous investigations on the dynamical stability of barotropic stars and collisionless stellar systems. A barotropic star that minimizes the energy functional at fixed mass is a nonlinearly dynamically stable stationary…
We consider the Vlasov-Poisson system in a cosmological setting and prove nonlinear stability of homogeneous solutions against small, spatially periodic perturbations in the sup-norm of the spatial mass density. This result is connected…
This paper considers the problem of robust stability for a class of uncertain nonlinear quantum systems subject to unknown perturbations in the system Hamiltonian. The case of a nominal linear quantum system is considered with non-quadratic…
We study the continuity of weak solutions for quasilinear elliptic systems with source terms of critical growth arising from a transport-energy structure. The latter occurs frequently in connection with the first balance principles of…
A class of periodic solutions of the nonlinear Schrodinger equation with non- Hermitian potentials are considered. The system may be implemented in planar nonlinear optical waveguides carrying an appropriate distribution of local gain and…
This paper investigates the existence of weak solutions of biquasilinear boundary value problem for a coupled elliptic-parabolic system of divergence form with discontinuous leading coefficients. The mathematical framework addressed in the…
The detonation wave stability is addressed using Fickett's equation, i.e., the reactive form of Burgers' equation. This serves as a simple analogue to the reactive Euler equations, permitting one to gain insight into the nonlinear dynamics…
Two-dimensional free-surface flow over localised topography is examined with the emphasis on the stability of hydraulic-fall solutions. A Gaussian topography profile is assumed with a positive or negative amplitude modelling a bump or a…