A semidiscretization scheme for a phase-field type model for solidification.
A semilinear control problem involving homogenization.
A semi-linear elliptic equation in a strip arising in a two-dimensional flame propagation model.
A semilinear equation in
A semilinear parabolic boundary-value problem in bioreactors theory.
A sharp Strichartz estimate for the wave equation with data in the energy space
We prove a sharp bilinear estimate for the wave equation from which we obtain the sharp constant in the Strichartz estimate which controls the norm of the solution in terms of the energy. We also characterise the maximisers.
A short note on theory for Stokes problem with a pressure-dependent viscosity
We study higher local integrability of a weak solution to the steady Stokes problem. We consider the case of a pressure- and shear-rate-dependent viscosity, i.e., the elliptic part of the Stokes problem is assumed to be nonlinear and it depends on and on the symmetric part of a gradient of , namely, it is represented by a stress tensor which satisfies -growth condition with . In order to get the main result, we use Calderón-Zygmund theory and the method which was presented for example in...
A singular ODE related to quasilinear elliptic equations.
A singular perturbation problem in a system of nonlinear Schrödinger equation occurring in Langmuir turbulence
The aim of this work is to establish, from a mathematical point of view, the limit α → +∞ in the system where . This corresponds to an approximation which is made in the context of Langmuir turbulence in plasma Physics. The L2-subcritical σ (that is σ ≤ 2/3) and the H1-subcritical σ (that is σ ≤ 2) are studied. In the physical case σ = 1, the limit is then studied for the norm.
A singular radially symmetric problem in electrolytes theory
Existence of radially symmetric solutions (both stationary and time dependent) for a parabolic-elliptic system describing the evolution of the spatial density of ions in an electrolyte is studied.
A smoothing property for the -critical NLS equations and an application to blowup theory
A spatially periodic Kuramoto-Sivashinsky equation as a model problem for inclined film flow over wavy bottom.
A spherical Harnack inequality for singular solutions of nonlinear elliptic equations
A stability estimate for a solution to a three-dimensional inverse problem for the Maxwell equations.
A stability estimate for a solution to the wave equation with the Cauchy data on a timelike cylindrical surface.
A stability result for -harmonic systems with discontinuous coefficients.
A stability result for parameter identification problems in nonlinear parabolic problems.
A stable manifold theorem for the gradient flow of geometric variational problems associated with quasi-linear parabolic equations
A strong maximum principle for the Paneitz operator and a non-local flow for the -curvature
In this paper we consider Riemannian manifolds of dimension , with semi-positive -curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green’s function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive -curvature. Modifying the test function construction of Esposito-Robert, we show...
A subsolution-supersolution method for quasilinear systems.