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 and weak stability for multi-dimensional transport equations with one-sided Lipschitz coefficient
The Cauchy problem for a multidimensional linear transport equation with discontinuous coefficient is investigated. Provided the coefficient satisfies a one-sided Lipschitz condition, existence, uniqueness and weak stability of solutions are obtained for either the conservative backward problem or the advective forward problem by duality. Specific uniqueness criteria are introduced for the backward conservation equation since weak solutions are not unique. A main point is the introduction of a generalized...
Uniqueness for a semilinear elliptic equation in non-contractible domains under supercritical growth conditions.
Uniqueness for first-order hyperbolic systems - with applications to secnd-order elliptic third-order and Maxwell's equations.
Uniqueness for positive solutions of -Laplacian problem in an annulus
Uniqueness for the two-dimensional semiconductor equations in case of high carrier densities.
Uniqueness of critical points for semi-linear Dirichlet problems in convex domains.
Uniqueness of global positive solution branches of nonlinear elliptic problems.
Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains
Uniqueness of solutions for some elliptic equations with a quadratic gradient term
We study a comparison principle and uniqueness of positive solutions for the homogeneous Dirichlet boundary value problem associated to quasi-linear elliptic equations with lower order terms. A model example is given by The main feature of these equations consists in having a quadratic gradient term in which singularities are allowed. The arguments employed here also work to deal with equations having lack of ellipticity or some dependence on u in the right hand side. Furthermore, they...
Uniqueness of solutions to degenerate elliptic problems with unbounded coefficients
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 critical mass blow up solution for the four dimensional gravitational Vlasov–Poisson system
Uniqueness of the Solution of a Semilinear Boundary Value Problem.
Uniqueness of weak solution for nonlinear elliptic equations in divergence form.
Univalent solutions of elliptic systems of Heinz-Lewy type
Univalent -harmonic mappings : applications to composites
This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all...
Univalent σ-harmonic mappings: applications to composites
This paper is part of a larger project initiated with [2]. The final aim of the present paper is to give bounds for the homogenized (or effective) conductivity in two dimensional linear conductivity. The main focus is therefore the periodic setting. We prove new variational principles that are shown to be of interest in finding bounds on the homogenized conductivity. Our results unify previous approaches by the second author and make transparent the central role of quasiconformal mappings in all...
Universal bounds for global solutions of a diffusion equation with a mixed local-nonlocal reaction term.