Nonlinear elliptic equations on compact Riemannian manifolds and asymptotics of Emden equations.
Nonlinear evolution inclusions arising from phase change models
The paper is devoted to the analysis of an abstract evolution inclusion with a non-invertible operator, motivated by problems arising in nonlocal phase separation modeling. Existence, uniqueness, and long-time behaviour of the solution to the related Cauchy problem are discussed in detail.
Nonlinear evolution PDEs in : existence and uniqueness of solutions, asymptotic and Borel summability properties
Nonlinear feedback stabilization of a rotating body-beam without damping
Nonlinear feedback stabilization of a rotating body-beam without damping
This paper deals with nonlinear feedback stabilization problem of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends the linear...
Nonlinear Heat Equation with a Fractional Laplacian in a Disk
For the nonlinear heat equation with a fractional Laplacian , 1 < α ≤ 2, the first initial-boundary value problem in a disk is considered. Small initial conditions, homogeneous boundary conditions, and periodicity conditions in the angular coordinate are imposed. Existence and uniqueness of a global-in-time solution is proved, and the solution is constructed in the form of a series of eigenfunctions of the Laplace operator in the disk. First-order long-time asymptotics of the solution is obtained....
Nonlinear integroparabolic equations on unbounded domains: existence of classical solutions with special properties.
Nonlinear models of suspension bridges: discussion of the results
In this paper we present several nonlinear models of suspension bridges; most of them have been introduced by Lazer and McKenna. We discuss some results which were obtained by the authors and other mathematicians for the boundary value problems and initial boundary value problems. Our intention is to point out the character of these results and to show which mathematical methods were used to prove them instead of giving precise proofs and statements.
Nonlinear nonautonomous partial functional differential BVP.
Nonlinear nonlocal evolution problems.
We consider a class of nonlinear parabolic problems where the coefficients are depending on a weighted integral of the solution. We address the issues of existence, uniqueness, stationary solutions and in some cases asymptotic behaviour.
Nonlinear parabolic problems on manifolds, and a nonexistence result for the noncompact Yamabe problem.
Nonlinear pseudodifferential equations on a half-line with large initial data.
Nonlinear Pulse Propagation
This talk gives a brief review of some recent progress in the asymptotic analysis of short pulse solutions of nonlinear hyperbolic partial differential equations. This includes descriptions on the scales of geometric optics and diffractive geometric optics, and also studies of special situations where pulses passing through focal points can be analysed.
Nonlinear Scattering for Some Dispersive Equations Generalizing Benjamin-Bona-Mahony Equation.
Nonlinear stability of a quasi-static Stefan problem with surface tension : a continuation approach
Nonlinear transmission problem with a dissipative boundary condition of memory type.
Nonlocal quadratic evolution problems
Nonlinear nonlocal parabolic equations modeling the evolution of density of mutually interacting particles are considered. The inertial type nonlinearity is quadratic and nonlocal while the diffusive term, also nonlocal, is anomalous and fractal, i.e., represented by a fractional power of the Laplacian. Conditions for global in time existence versus finite time blow-up are studied. Self-similar solutions are constructed for certain homogeneous initial data. Monte Carlo approximation schemes by interacting...
Nonradial solutions of nonlinear Neumann problems in radially symmetric domains
Non-standard applications of the Łojasiewicz-Simon theory: Stabilization to equilibria of solutions to phase-field models
This is a survey of results on the long-time behavior of solutions to phase-field models and related problems. The central idea is based on several non-standard applications of the Łojasiewicz-Simon theory.
Normal form and global solutions for the Klein-Gordon-Zakharov equations