Su alcune equazioni differenziali astratte di tipo degenere
Sul problema di Cauchy-Neumann per le equazioni paraboliche singolari a coefficienti discontinue in due variabili
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.
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...
Support re-splitting phenomena caused by an interaction between diffusion and absorption
Sur l’équation générale dans : II. Le problème d’évolution
Sur un problème parabolique-elliptique
Sur un problème parabolique-elliptique
We prove existence (uniqueness is easy) of a weak solution to a boundary value problem for an equation like where the function is only supposed to be locally lipschitz continuous. In order to replace the lack of compactness in t on v<1, we use nonlinear semigroup theory.
Sur une classe de problèmes d'évolution quasi linéaires dégénérés.
Sur une classe d'équations paraboliques dégénérées
The a priori estimate of the maximum modulus to solutions of doubly nonlinear parabolic equations
The a priori estimate of the maximum modulus of the generalized solution is established for a doubly nonlinear parabolic equation with special structural conditions.
The Cauchy problem and steady state solutions for a nonlocal Cahn-Hilliard equation.
The Cauchy problem for a strongly degenerate quasilinear equation
We prove existence and uniqueness of entropy solutions for the Cauchy problem for the quasilinear parabolic equation , where , and is a convex function of with linear growth as , satisfying other additional assumptions. In particular, this class includes a relativistic heat equation and a flux limited diffusion equation used in the theory of radiation hydrodynamics.
The Cauchy problem for degenerate parabolic equations in Gevrey classes
The dipole solution for the porous medium equation in several space dimensions
The Dirichlet problem for a class of nonlinear degenerate parabolic equations.
The finite speed of propagation of solutions of the Neumann problem of a degenerate parabolic equation
In this paper the finite speed of propagation of solutions and the continuous dependence on the nonlinearity of a degenerate parabolic partial differential equation are discussed. Our objective is to derive an explicit expression for the speed of propagation and the large time behavior of the solution and to show that the solution continuously depends on the nonlinearity of the equation.
The version of Eulerian-Lagrangian mixed discontinuous finite element methods for advection-diffusion problems.
The local solution of a parabolic-elliptic equation with a nonlinear Neumann boundary condition
We investigate a parabolic-elliptic problem, where the time derivative is multiplied by a coefficient which may vanish on time-dependent spatial subdomains. The linear equation is supplemented by a nonlinear Neumann boundary condition with a locally defined, -bounded function . We prove the existence of a local weak solution to the problem by means of the Rothe method. A uniform a priori estimate for the Rothe approximations in , which is required by the local assumptions on , is derived by...
The Mumford-Shah conjecture in image processing