Uniqueness and stability of regional blow-up in a porous-medium equation
Uniqueness and stability of solutions for a type of parabolic boundary value problem.
Uniqueness and stability properties of monostable pulsating fronts
We prove the uniqueness, up to shifts, of pulsating traveling fronts for reaction-diffusion equations in periodic media with Kolmogorov–Petrovskiĭ–Piskunov type nonlinearities. These results provide in particular a complete classification of all KPP pulsating fronts. Furthermore, in the more general case of monostable nonlinearities, we also derive several global stability properties and convergence to pulsating fronts for solutions of the Cauchy problem with front-like initial data. In particular,...
Uniqueness for a boundary identification problem in thermal imaging.
Uniqueness for the harmonic map flow from surface to general targets.
Uniqueness for the two-dimensional semiconductor equations in case of high carrier densities.
Uniqueness of bounded solutions to a viscous diffusion equation.
Uniqueness of entropy solutions of nonlinear elliptic-parabolic-hyperbolic problems in one dimension space.
Uniqueness of entropy solutions to nonlinear elliptic-parabolic problems.
Uniqueness of Monotone Mono-stable Waves for Reaction-Diffusion Equations with Time Delay
Many models in biology and ecology can be described by reaction-diffusion equations wit time delay. One of important solutions for these type of equations is the traveling wave solution that shows the phenomenon of wave propagation. The existence of traveling wave fronts has been proved for large class of equations, in particular, the monotone systems, such as the cooperative systems and some competition systems. However, the problem on the uniqueness of traveling wave (for a fixed wave speed)...
Uniqueness of motion by mean curvature perturbed by stochastic noise
Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains
Uniqueness of solution of a singular heat equation.
Uniqueness of solutions of a mixed problem for parabolic differential-functional equations
Uniqueness of solutions to a class of strongly degenerate parabolic equation.
Uniqueness of solutions to a system of differential inclusions.
Uniqueness of the boundary behavior for large solutions to a degenerate elliptic equation involving the ∞-Laplacian.
En esta nota estimamos la tasa máxima de crecimiento en la frontera de las soluciones de viscosidad de -Δ∞u + λ|u|m-1u = f en Ω (λ > 0, m > 3).De hecho, mostramos que sólo hay una única tasa de explosión en la frontera para esas soluciones explosivas. También obtenemos una versión del Teorema de Liouville para el caso Ω = RN.
Uniqueness of the solution of the Cauchy problem to some equations of nonstationary filtration
Uniqueness of very singular self-similar solution of a quasilinear degenerate parabolic equation with absorption.
We show the uniqueness of the very singular self-similar solution of the equationut - Δ pum + uq = 0.The result is carried out by studying the stationary associate equation and by introducing a suitable change of unknown. That allows to assume the zero-order perturbation term in the new equation to be monotone increasing. A careful study of the behaviour of solutions near the boundary of their support is also used in order to prove the main result.
Uniqueness results for some PDEs
Existence of solutions to many kinds of PDEs can be proved by using a fixed point argument or an iterative argument in some Banach space. This usually yields uniqueness in the same Banach space where the fixed point is performed. We give here two methods to prove uniqueness in a more natural class. The first one is based on proving some estimates in a less regular space. The second one is based on a duality argument. In this paper, we present some results obtained in collaboration with Pierre-Louis...