Convergence of an entropic semi-discretization for nonlinear Fokker-Planck equations in Rd
Convergence of Rothe's method in Hölder spaces
The convergence of Rothe’s method in Hölder spaces is discussed. The obtained results are based on uniform boundedness of Rothe’s approximate solutions in Hölder spaces recently achieved by the first author. The convergence and its rate are derived inside a parabolic cylinder assuming an additional compatibility conditions.
Decay estimates for solutions of a class of parabolic problems arising in filtration through porous media
In questo lavoro si studia un problema di valori al contorno parabolico non lineare che si incontra nello studio dell'infiltrazione di un gas in un mezzo poroso. Si stabiliscono condizioni sui dati che determinano un comportamento di tipo esponenziale decrescente nel tempo per la soluzione e il suo gradiente. Si costruiscono inoltre stime esplicite.
Differential-functional inequalities of parabolic type in unbounded regions
Discrete maximum principle for interior penalty discontinuous Galerkin methods
A class of linear elliptic operators has an important qualitative property, the so-called maximum principle. In this paper we investigate how this property can be preserved on the discrete level when an interior penalty discontinuous Galerkin method is applied for the discretization of a 1D elliptic operator. We give mesh conditions for the symmetric and for the incomplete method that establish some connection between the mesh size and the penalty parameter. We then investigate the sharpness of...
Discrete maximum principles for the FEM solution of some nonlinear parabolic problems.
Ein Maximumprinzip für nichtlineare parabolische Systeme.
Estimates for smooth absolutely minimizing Lipschitz extensions.
Estimates of weak solutions to nondiagonal quasilinear parabolic systems
-estimates of weak solutions are established for a quasilinear non-diagonal parabolic system with a special structure whose leading terms are modelled by p-Laplacians. A generalization of the weak maximum principle to systems of equations is employed.
Estimation des valeurs propres d'opérateurs elliptiques sur des ouverts non bornés
Evolutionary Games in Space
The G-function formalism has been widely used in the context of evolutionary games for identifying evolutionarily stable strategies (ESS). This formalism was developed for and applied to point processes. Here, we examine the G-function formalism in the settings of spatial evolutionary games and strategy dynamics, based on reaction-diffusion models. We start by extending the point process maximum principle to reaction-diffusion models with homogeneous, locally stable surfaces. We then develop...
Existence and multiplicity of solutions to elliptic problems with discontinuities and free boundary conditions.
Existence and uniqueness of Lipschitz continuous graphs with prescribed Levi curvature
Existence and Uniqueness of Solutions of Nonlinear Neumann Problems.
Existence and uniqueness results of positive solutions for nonvariational quasilinear elliptic systems.
Existence of infinitely many solutions for elliptic boundary-value problems with nonsymmetrical critical nonlinearity.
Existence of solutions for non-necessarily cooperative systems involving Schrödinger operators.
Existence of Waves for a Nonlocal Reaction-Diffusion Equation
In this work we study a nonlocal reaction-diffusion equation arising in population dynamics. The integral term in the nonlinearity describes nonlocal stimulation of reproduction. We prove existence of travelling wave solutions by the Leray-Schauder method using topological degree for Fredholm and proper operators and special a priori estimates of solutions in weighted Hölder spaces.
Existence results for quasilinear problems via ordered sub and supersolutions
Existences and boundary behavior of boundary blow-up solutions to quasilinear elliptic systems with singular weights.