A local version of the generalized retract theorem of Ważewski with applications in the theory of partial differential equations of first order
Connecting orbits of time dependent Lagrangian systems
We generalize to higher dimension results of Birkhoff and Mather on the existence of orbits wandering in regions of instability of twist maps. This generalization is strongly inspired by the one proposed by Mather. However, its advantage is that it contains most of the results of Birkhoff and Mather on twist maps.
Example of solving of the boundary value problems for one partial differential equations with two unknown functions
Free Boundary Problems Associated with Multiscale Tumor Models
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...
Hydrodynamical limit for the asymmetric zero-range process
On the Chaplygin method for partial differential-functional equations of the first order
Sur l'unicité du prolongement des systèmes elliptiques dont la valeur initiale s'annule sur un sous-ensemble de mesure positive
The solution of embedding problems in the framework of GAPs with applications on nonlinear PDEs.
О преобразованиях первых интегралов двух дифференциальных уравнений в частных производных первого порядка