Stability of global solutions to one-phase Stefan problem for a semilinear parabolic equation
Stability of radially symmetric travelling waves in reaction–diffusion equations
Stabilization of solutions for semilinear parabolic systems as .
Stabilization of walls for nano-wires of finite length
In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.
Stabilization of walls for nano-wires of finite length
In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.
Stabilization of walls for nano-wires of finite length
In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field.
Stabilizing influence of a Skew-symmetric operator in semilinear parabolic equation
Starke Lösungen semilinearer parabolischer Differentialgleichungen.
Stochastic representations of derivatives of solutions of one-dimensional parabolic variational inequalities with Neumann boundary conditions
In this paper we explicit the derivative of the flows of one-dimensional reflected diffusion processes. We then get stochastic representations for derivatives of viscosity solutions of one-dimensional semilinear parabolic partial differential equations and parabolic variational inequalities with Neumann boundary conditions.
Strong maximum and minimum principles for parabolic functional-differential problems with initial inequalities
Strong maximum and minimum principles for parabolic functional-differential problems with nonlocal inequalities
Strong maximum principle for non-linear parabolic differential-functional inequalities
Strong maximum principle for non-linear parabolic differential-functional inequalities in arbitrary domains
Strong maximum principles for parabolic nonlinear problems with nonlocal inequalities together with integrals.
Study of a three component Cahn-Hilliard flow model
In this paper, we propose a new diffuse interface model for the study of three immiscible component incompressible viscous flows. The model is based on the Cahn-Hilliard free energy approach. The originality of our study lies in particular in the choice of the bulk free energy. We show that one must take care of this choice in order for the model to give physically relevant results. More precisely, we give conditions for the model to be well-posed and to satisfy algebraically and dynamically consistency...
Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems
We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas...
Sufficient conditions for nonexistence of gradient blow-up for nonlinear parabolic equations.
Summability of semicontinuous supersolutions to a quasilinear parabolic equation
We study the so-called -superparabolic functions, which are defined as lower semicontinuous supersolutions of a quasilinear parabolic equation. In the linear case, when , we have supercaloric functions and the heat equation. We show that the -superparabolic functions have a spatial Sobolev gradient and a sharp summability exponent is given.
Summation of polyparametrical functional series by the method of finite hybrid integral transforms (Fourier, Bessel)
Super and ultracontractive bounds for doubly nonlinear evolution equations.
We use logarithmic Sobolev inequalities involving the p-energy functional recently derived in [15], [21] to prove Lp-Lq smoothing and decay properties, of supercontractive and ultracontractive type, for the semigroups associated to doubly nonlinear evolution equations of the form u· = Δp(um) (with m(p - 1) ≥ 1) in an arbitrary euclidean domain, homogeneous Dirichlet boundary conditions being assumed. The bound are of the form ||u(t)||q ≤ C||u0||rγ / tβ for any r ≤ q ∈ [1,+∞) and t > 0 and...