Damped wave equations and the heat equation
Das Cauchy-Problem bei quasilinearen parabolischen Differentialgleichungen mit unstetigen Anfangswerten.
Das Lemma von Max Müller-Nagumo-Westphal für stark gekoppelte Systeme parabolischer Funktional-Differentialgleichungen.
Das Maximumprinzip in unbeschränkten Gebieten für parabolische Ungleichungen mit Funktionalen.
Decay and asymptotic behavior of solutions of the Keller-Segel system of degenerate and nondegenerate type
We classify the global behavior of weak solutions of the Keller-Segel system of degenerate and nondegenerate type. For the stronger degeneracy, the weak solution exists globally in time and has a uniform time decay under some extra conditions. If the degeneracy is weaker, the solution exhibits a finite time blow up if the data is nonnegative. The situation is very similar to the semilinear case. Some additional discussion is also presented.
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.
Decay rates for solutions of damped systems and generalized Fourier transforms.
Decay rates for solutions of degenerate parabolic systems.
Deep learning for gradient flows using the Brezis–Ekeland principle
We propose a deep learning method for the numerical solution of partial differential equations that arise as gradient flows. The method relies on the Brezis–Ekeland principle, which naturally defines an objective function to be minimized, and so is ideally suited for a machine learning approach using deep neural networks. We describe our approach in a general framework and illustrate the method with the help of an example implementation for the heat equation in space dimensions two to seven.
Defibrillation in models of cardiac muscle.
Deforming convex hypersurfaces by the square root of the scalar curvature.
Deforming Hypersurfaces of the Sphere by Their Mean Curvature.
Degenerate diffusive SEIR model with logistic population control.
Degenerate stationary problems with homogeneous boundary conditions.
Degenerate triply nonlinear problems with nonhomogeneous boundary conditions
The paper addresses the existence and uniqueness of entropy solutions for the degenerate triply nonlinear problem: b(v)t − div α(v, ▽g(v)) = f on Q:= (0, T) × Ω with the initial condition b(v(0, ·)) = b(v 0) on Ω and the nonhomogeneous boundary condition “v = u” on some part of the boundary (0, T) × ∂Ω”. The function g is continuous locally Lipschitz continuous and has a flat region [A 1, A 2,] with A 1 ≤ 0 ≤ A 2 so that the problem is of parabolic-hyperbolic type.
Degenerate two-phase incompressible flow problems III: Perturbation analysis and numerical experiments.
Degenerating Cahn-Hilliard systems coupled with mechanical effects and complete damage processes
This paper addresses analytical investigations of degenerating PDE systems for phase separation and damage processes considered on nonsmooth time-dependent domains with mixed boundary conditions for the displacement field. The evolution of the system is described by a degenerating Cahn-Hilliard equation for the concentration, a doubly nonlinear differential inclusion for the damage variable and a quasi-static balance equation for the displacement field. The analysis is performed on a time-dependent...
Degeneration of effective diffusion in the presence of periodic potential
Dépendance continue de solutions généralisées locales
Derivation of a homogenized two-temperature model from the heat equation
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat,...