5-Shaped Bifurcation Curves of Nonlinear Elliptic Boundary Value Problems.
A Class of Elliptic Partial Differential Equations with Exponential Nonlinearities.
A complement to the Fredholm theory of elliptic systems on bounded domains.
A Counter-Example to the Boundary Regularity of Solutions to Elliptic Quasilinear Systems.
A first order partial differential equation with an integral boundary condition
In questo lavoro si considera un’equazione alle derivate parziali del primo ordine con una condizione sulla frontiera di tipo integrale. Si studia resistenza, l'unicità e il comportamento asintotico delle soluzioni.
A global continuation theorem for obtaining eigenvalues and bifurcation points
A Hopf bifurcation generated by variation of the domain
A locally contractive metric for systems of conservation laws
A mixed problem with only integral boundary conditions for a hyperbolic equation.
A nonexistence test for biharmonic Green's functions of clamped bodies.
A nonlinear wave equation with a nonlinear integral equation involving the boundary value.
A qualitative study on a parabolic free boundary problem.
A remark concerning the dependence on the initial data of the solution of the Cauchy problem for a linear equation with analytic coefficients
A Remark on a boundary contact problem in linear elasticity.
A Uniqueness Theorem for Some Nonlinear Boundary Value Problems with a Large Parameter.
A variational inequality for discontinuous solutions of degenerate parabolic equations.
The Beltrami framework for image processing and analysis introduces a non-linear parabolic problem, called in this context the Beltrami flow. We study in the framework for functions of bounded variation, the well-posedness of the Beltrami flow in the one-dimensional case. We prove existence and uniqueness of the weak solution using lower semi-continuity results for convex functions of measures. The solution is defined via a variational inequality, following Temam?s technique for the evolution problem...
About the influence of oscillations on Strichartz-type decay estimates.
Addendum to "The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation"
In this addendum we address some unintentional omission in the description of the swimming model in our recent paper (Khapalov, 2013).
Almost sure global well-posedness for the radial nonlinear Schrödinger equation on the unit ball II: the 3d case
We extend the convergence method introduced in our works [8–10] for almost sure global well-posedness of Gibbs measure evolutions of the nonlinear Schrödinger (NLS) and nonlinear wave (NLW) equations on the unit ball in to the case of the three dimensional NLS. This is the first probabilistic global well-posedness result for NLS with supercritical data on the unit ball in . The initial data is taken as a Gaussian random process lying in the support of the Gibbs measure associated to the equation,...
Almost sure well-posedness for the periodic 3D quintic nonlinear Schrödinger equation below the energy space
We also prove a long time existence result; more precisely we prove that for fixed there exists a set , such that any data , evolves up to time into a solution with , . In particular we find a nontrivial set of data which gives rise to long time solutions below the critical space , that is in the supercritical scaling regime.