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Displaying 121 – 140 of 401

Free Boundary Problems Associated with Multiscale Tumor Models

A. Friedman (2009)

Mathematical Modelling of Natural Phenomena

The present paper introduces a tumor model with two time scales, the time t during which the tumor grows and the cycle time of individual cells. The model also includes the effects of gene mutations on the population density of the tumor cells. The model is formulated as a free boundary problem for a coupled system of elliptic, parabolic and hyperbolic equations within the tumor region, with nonlinear and nonlocal terms. Existence and uniqueness theorems are proved, and properties of the free boundary...

Frentes de explosión en ecuaciones de Hamilton Jacobi por argumentos de control determinista.

G. Díaz (1989)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

Functional differential equations with non-local boundary conditions.

Guezane-Lakoud, Assia (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Funzioni $(p,q)$ -convesse

Ennio De Giorgi, Antonio Marino, Mario Tosques (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We study a class of functions which differ essentially from those which are the sum of a convex function and a regular one and which have interesting properties related to $\Gamma$ -convergence and to problems with non-convex constraints. In particular some results are given for the associated evolution equations.

Generalized Cauchy problems for hyperbolic functional differential systems

Elżbieta Puźniakowska-Gałuch (2014)

Annales Polonici Mathematici

A generalized Cauchy problem for hyperbolic functional differential systems is considered. The initial problem is transformed into a system of functional integral equations. The existence of solutions of this system is proved by using the method of successive approximations. Differentiability of solutions with respect to initial functions is proved. It is important that functional differential systems considered in this paper do not satisfy the Volterra condition.

Generalized Dirac Operators on Nonsmooth Manifolds and Maxwell's Equations.

Marius Mitrea (2001)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

Generalized gradient flow and singularities of the Riemannian distance function

Piermarco Cannarsa (2012/2013)

Séminaire Laurent Schwartz — EDP et applications

Significant information about the topology of a bounded domain $Ω$ of a Riemannian manifold $M$ is encoded into the properties of the distance, $d_{\partial Ω}$ , from the boundary of $Ω$ . We discuss recent results showing the invariance of the singular set of the distance function with respect to the generalized gradient flow of $d_{\partial Ω}$ , as well as applications to homotopy equivalence.

Generalized solutions by Cauchy's method of characteristics

Ştefan Mirică (1987)

Rendiconti del Seminario Matematico della Università di Padova

Generalized Solutions to Nonlinear First-Order Systems.

H.A. Biagioni (1994)

Monatshefte für Mathematik

Geometric restrictions for the existence of viscosity solutions

P. Cardaliaguet, B. Dacorogna, W. Gangbo, N. Georgy (1999)

Annales de l'I.H.P. Analyse non linéaire

Germes de configurations legendriennes stables et fonctions d'Airy-Weber généralisées

Nguyen Hu'u Du'c, Frédéric Pham (1991)

Annales de l'institut Fourier

On sait depuis Maslov, Arnold, etc... associer à presque tout germe de variété lagrangienne ou legendrienne lisse une classe de fonctions oscillantes qui sous des hypothèses génériques à la Thom fournissent des modèles universels pour le comportement d’une onde lumineuse au voisinage de la caustique.Le présent article étend cette construction à une classe de situations où la variété caractéristique est un germe singulier (union de composantes lisses), qui peut néanmoins être stable en ce sens que...

Global analytic and Gevrey surjectivity of the Mizohata operator $D_{2} + i x_{2}^{2 k} D_{1}$

L. Cattabriga, L. Zanghirati (1989)

Journées équations aux dérivées partielles

Global analytic and Gevrey surjectivity of the Mizohata operator $D_{2} + i x_{2}^{2 k} D_{1}$

Lamberto Cattabriga, Luisa Zanghirati (1990)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The surjectivity of the operator $D_{2} + i x_{2}^{2 k} D_{1}$ from the Gevrey space $E^{\{s\}} (R^{2})$ , $s \geq 1$ , onto itself and its non-surjectivity from $E^{\{s\}} (R^{3})$ to $E^{\{s\}} (R^{3})$ is proved.

Global existence for non-linear partial differential equations of the first order

A. Adamus-Kulczycka (1973)

Annales Polonici Mathematici

Global smooth solutions of some quasi-linear hyperbolic systems with large data

F. Poupaud (1999)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Global subanalytic solutions of Hamilton–Jacobi type equations

Emmanuel Trélat (2006)

Annales de l'I.H.P. Analyse non linéaire

Hamilton-Jacobi flows and characterization of solutions of Aronsson equations

Petri Juutinen, Eero Saksman (2007)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this note, we verify the conjecture of Barron, Evans and Jensen [3] regarding the characterization of viscosity solutions of general Aronsson equations in terms of the properties of associated forward and backwards Hamilton-Jacobi flows. A special case of this result is analogous to the characterization of infinity harmonic functions in terms of convexity and concavity of the functions $r \mapsto {max}_{y \in B_{r} (x)} u (y)$ and $r \mapsto {min}_{y \in B_{r} (x)} u (y)$ , respectively.

Hardy and Hardy-Sobolev Spaces on Strongly Lipschitz Domains and Some Applications

Xiaming Chen, Renjin Jiang, Dachun Yang (2016)

Analysis and Geometry in Metric Spaces

Let Ω ⊂ Rn be a strongly Lipschitz domain. In this article, the authors study Hardy spaces, Hpr (Ω)and Hpz (Ω), and Hardy-Sobolev spaces, H1,pr (Ω) and H1,pz,0 (Ω) on , for p ∈ ( n/n+1, 1]. The authors establish grand maximal function characterizations of these spaces. As applications, the authors obtain some div-curl lemmas in these settings and, when is a bounded Lipschitz domain, the authors prove that the divergence equation div u = f for f ∈ Hpz (Ω) is solvable in H1,pz,0 (Ω) with suitable...

Homogenization and localization in locally periodic transport

Grégoire Allaire, Guillaume Bal, Vincent Siess (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we study the homogenization and localization of a spectral transport equation posed in a locally periodic heterogeneous domain. This equation models the equilibrium of particles interacting with an underlying medium in the presence of a creation mechanism such as, for instance, neutrons in nuclear reactors. The physical coefficients of the domain are $ε$ -periodic functions modulated by a macroscopic variable, where $ε$ is a small parameter. The mean free path of the particles is also...

Homogenization and localization in locally periodic transport

Grégoire Allaire, Guillaume Bal, Vincent Siess (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we study the homogenization and localization of a spectral transport equation posed in a locally periodic heterogeneous domain. This equation models the equilibrium of particles interacting with an underlying medium in the presence of a creation mechanism such as, for instance, neutrons in nuclear reactors. The physical coefficients of the domain are ε-periodic functions modulated by a macroscopic variable, where ε is a small parameter. The mean free path of the particles...

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