A fundamental estimate and an inequality of Caccioppoli's type for nonlinear parabolic systems of higher order
A generalization of the maximum principle to nonlinear parabolic systems
A generalization of the well-known weak maximum principle is established for a class of quasilinear strongly coupled parabolic systems with leading terms of p-Laplacian type.
A mathematical model for the recovery of human and economic activities in disaster regions
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
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...
A topological invariant arising in the stability analysis of travelling waves.
Almost periodic solutions to systems of parabolic equations.
Autowaves in the Model of Infiltrative Tumour Growth with Migration-Proliferation Dichotomy
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
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...