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A mathematical model for the recovery of human and economic activities in disaster regions

Atsushi Kadoya, Nobuyuki Kenmochi (2014)

Mathematica Bohemica

In this paper a model for the recovery of human and economic activities in a region, which underwent a serious disaster, is proposed. The model treats the case that the disaster region has an industrial collaboration with a non-disaster region in the production system and, especially, depends upon each other in technological development. The economic growth model is based on the classical theory of R. M. Solow (1956), and the full model is described as a nonlinear system of ordinary differential...

A solution of nonlinear diffusion problems by semilinear reaction-diffusion systems

Hideki Murakawa (2009)

Kybernetika

This paper deals with nonlinear diffusion problems involving degenerate parabolic problems, such as the Stefan problem and the porous medium equation, and cross-diffusion systems in population ecology. The degeneracy of the diffusion and the effect of cross-diffusion, that is, nonlinearities of the diffusion, complicate its analysis. In order to avoid the nonlinearities, we propose a reaction-diffusion system with solutions that approximate those of the nonlinear diffusion problems. The reaction-diffusion...

Autowaves in the Model of Infiltrative Tumour Growth with Migration-Proliferation Dichotomy

A.V. Kolobov, V.V. Gubernov, A.A. Polezhaev (2011)

Mathematical Modelling of Natural Phenomena

A mathematical model of infiltrative tumour growth is investigated taking into account transitions between two possible states of malignant cells: proliferation and migration. These transitions are considered to depend on oxygen level in a threshold manner where high oxygen concentration allows cell proliferation, while concentration below a certain critical value induces cell migration. The infiltrative tumour spreading rate dependence on model parameters is obtained. It is shown that the tumour...

Axiomatique des fonctions biharmoniques. II

Emmanuel P. Smyrnelis (1976)

Annales de l'institut Fourier

Dans un espace biharmonique, on définit un balayage de couples de mesures et, en particulier, on retrouve les trois mesures du problème de Riquier. Une de ces mesures n’étant pas harmonique, son étude présente un certain intérêt. On établit, dans ce cadre, des inégalités de type Harnack et on introduit les fonctions hyperharmoniques d’ordre 2. Le problème de la construction d’un espace biharmonique à partir de deux espaces harmoniques est aussi étudié. Enfin, on donne des applications de la théorie...

Boundary value problems and duality between Lp Dirichlet and regularity problems for second order parabolic systems in non-cylindrical domains.

Kaj Nyström (2006)

Collectanea Mathematica

In this paper we consider general second order, symmetric and strongly elliptic parabolic systems with real valued and constant coefficients in the setting of a class of time-varying, non-smooth infinite cylindersΩ = {(x0,x,t) ∈ R x Rn-1 x R: x0 > A(x,t)}.We prove solvability of Dirichlet, Neumann as well as regularity type problems with data in Lp and Lp1,1/2 (the parabolic Sobolev space having tangential (spatial) gradients and half a time derivative in Lp) for p ∈ (2 − ε, 2 + ε) assuming...

Characterization of the interior regularity for parabolic systems with discontinuous coefficients

Dian K. Palagachev, Lubomira G. Softova (2005)

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

We deal in this Note with linear parabolic (in sense of Petrovskij) systems of order 2 b with discontinuous principal coefficients belonging to V M O L . By means of a priori estimates in Sobolev-Morrey spaces we give a precise characterization of the Morrey, BMO and Hölder regularity of the solutions and their derivatives up to order 2 b - 1 .

Consistent models for electrical networks with distributed parameters

Corneliu A. Marinov, Gheorghe Moroşanu (1992)

Mathematica Bohemica

A system of one-dimensional linear parabolic equations coupled by boundary conditions which include additional state variables, is considered. This system describes an electric circuit with distributed parameter lines and lumped capacitors all connected through a resistive multiport. By using the monotony in a space of the form L 2 ( 0 , T ; H 1 ) , one proves the existence and uniqueness of a variational solution, if reasonable engineering hypotheses are fulfilled.

Differentiability of weak solutions of nonlinear second order parabolic systems with quadratic growth and nonlinearity q 2

Luisa Fattorusso (2004)

Commentationes Mathematicae Universitatis Carolinae

Let Ω be a bounded open subset of n , let X = ( x , t ) be a point of n × N . In the cylinder Q = Ω × ( - T , 0 ) , T > 0 , we deduce the local differentiability result u L 2 ( - a , 0 , H 2 ( B ( σ ) , N ) ) H 1 ( - a , 0 , L 2 ( B ( σ ) , N ) ) for the solutions u of the class L q ( - T , 0 , H 1 , q ( Ω , N ) ) C 0 , λ ( Q ¯ , N ) ( 0 < λ < 1 , N integer 1 ) of the nonlinear parabolic system - i = 1 n D i a i ( X , u , D u ) + u t = B 0 ( X , u , D u ) with quadratic growth and nonlinearity q 2 . This result had been obtained making use of the interpolation theory and an imbedding theorem of Gagliardo-Nirenberg type for functions u belonging to W 1 , q C 0 , λ .

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