On the second boundary value problem for equations of Monge-Ampère type.
On the semigroups of age-size dependent population dynamcis with spatial diffusion.
On the singularities of the solution of the Cauchy problem for the operator with non uniform multiple characteristics
On the Singularities of the Solution to the Cauchy Problem with Singular Data in the Complex Domain.
On the smoothness of viscosity solutions of the prescribed Levi-curvature equation
In this paper a -regularity result for the strong viscosity solutions to the prescribed Levi-curvature equation is announced. As an application, starting from a result by Z. Slodkowski and G. Tomassini, the -solvability of the Dirichlet problem related to the same equation is showed.
On the solvability of von Kármán equations
On the stability of solitary waves for classical scalar fields
On the support of solutions to the generalized KdV equation
On the Uniqueness of Solutions and on the Convergence of Successive Approximations for Certain Initial Problems of Equations of the Higher Orders
On the uniqueness of the Cauchy problem for partial differential operators with multiple characteristics
On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients
We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution....
On uniqueness and stability of steady-state carrier distributions in semiconductors
On weighted estimated for some systems of partial differential operators
Ondes semi-linéaires conormales classiques par rapport à deux hypersurfaces transverses
Opérateurs de Fuchs non linéaires
On se propose d’étudier des équations aux dérivées partielles non linéaires du type de Fuchs au sens de Baouendi-Goulaouic ([1] et [2]) dans des espaces de fonctions suffisamment différentiables par rapport à la variable fuchsienne et dans des espaces de Gevrey par rapport aux autres variables. Les méthodes utilisées reposent sur le formalisme des séries formelles Gevrey développé dans [13] et adapté aux équations du type de Fuchs dans [6] et [7]. On obtient ainsi des théorèmes qui généralisent...
Optimal control of the bidomain system (III): Existence of minimizers and first-order optimality conditions
We consider optimal control problems for the bidomain equations of cardiac electrophysiology together with two-variable ionic models, e.g. the Rogers–McCulloch model. After ensuring the existence of global minimizers, we provide a rigorous proof for the system of first-order necessary optimality conditions. The proof is based on a stability estimate for the primal equations and an existence theorem for weak solutions of the adjoint system.
Optimization of measurements for state estimation in parabolic distributed systems
Oscillation of solutions to a higher-order neutral PDE with distributed deviating arguments.
Oscillation theorems and nodes of eigenfunctions of certain differential equations of the fourth order
Parabolic equations with coefficients depending on t and parameters