Mixed problems for fully nonlinear hyperbolic equations.
Modelling bioremediation of polluted soils in unsaturated condition and its effect on the soil hydraulic properties
We study the unsaturated flow of an incompressible liquid carrying a bacterial population through a porous medium contaminated with some pollutant. The biomass grows feeding on the pollutant and affecting at the same time all the physics of the flow. We formulate a mathematical model in a one-dimensional setting and we prove an existence theorem for it. The so-called fluid media scaling approach, often used in the literature, is discussed and its limitations are pointed out on the basis of a specific...
Monotonicity in time and stationary solutions for a quasilinear heat equation with source.
Multiplicity results for a perturbed elliptic Neumann problem.
Multiplicity results of positive radial solutions for -Laplacian problems in exterior domains.
Nonexistence of Petrov type III space-times on which Weyl's neutrino equation or Maxwell's equations satisfy Huygens' principle
Non-homogeneous Neumann problems in domains with small holes
Nonlinear Elliptic Problems with Critical Exponent in Shrinking Annuli.
Nonlinear symmetric positive systems
Nonresonance Below the First Eigenvalue for a Semilinear Elliptic Problem.
Nonstrictly Hyperbolic Nonlinear Systems.
Non-unicité des solutions d'une équation d'évolution non-linéaire
Non-unicité du problème de Cauchy pour des opérateurs de type principal
Normal forms for parabolic partial differential equations
Numerical solutions of a fractional predator-prey system.
On a familiy of torsional creep problems.
On a mathematical model for the crystallization of polymers
We consider a mathematical model proposed in [1] for the cristallization of polymers, describing the evolution of temperature, crystalline volume fraction, number and average size of crystals. The model includes a constraint on the crystal volume fraction. Essentially, the model is a system of both second order and first order evolutionary partial differential equations with nonlinear terms which are Lipschitz continuous, as in [1], or Hölder continuous, as in [3]. The main novelty here is the...
On a mixed boundary values problem for Lavrentev type equations
On an over-determined problem of free boundary of a degenerate parabolic equation
This work is concerned with the inverse problem of determining initial value of the Cauchy problem for a nonlinear diffusion process with an additional condition on free boundary. Considering the flow of water through a homogeneous isotropic rigid porous medium, we have such desire: for every given positive constants and , to decide the initial value such that the solution satisfies , where . In this paper, we first establish a priori estimate and a more precise Poincaré type inequality...
On initial boundary value problem with Dirichlet integral conditions for a hyperbolic equation with the Bessel operator.