Error estimates of a linear approximation scheme for nonlinear diffusion problems.
Estimates of a stabilization rate as of solutions of a nonlinear integro-differential equation.
Estimates of weak solutions to nondiagonal quasilinear parabolic systems
-estimates of weak solutions are established for a quasilinear non-diagonal parabolic system with a special structure whose leading terms are modelled by p-Laplacians. A generalization of the weak maximum principle to systems of equations is employed.
Estimations uniformes à l’explosion pour les équations de la chaleur non linéaires et applications
Étude de l'existence de solutions globales d'un système de réaction-diffusion parabolique fortement non linéaire
Evolution of convex entire graphs by curvature flows
We consider the evolution of an entire convex graph in euclidean space with speed given by a symmetric function of the principal curvatures. Under suitable assumptions on the speed and on the initial data, we prove that the solution exists for all times and it remains a graph. In addition, after appropriate rescaling, it converges to a homothetically expanding solution of the flow. In this way, we extend to a class of nonlinear speeds the well known results of Ecker and Huisken for the mean curvature...
Evolution of subsets of and parabolic problem for the Levi equation
Exact Schauder estimates of solutions of a boundary value problem for parabolic second order equations and their application to a nonlinear problem
We establish exact Schauder estimates of solutions of the transmission problem for linear parabolic second order equations with explicit dependence on the smoothness of the coefficients. Next we apply the estimates to the solvability of the nonlinear transmission problem.
Existence and attractors of solutions for nonlinear parabolic systems.
Existence and construction of anisotropic solutions to the multidimensional equation of nonlinear diffusion. I.
Existence and decay of solutions of some nonlinear parabolic variational inequalities.
Existence and nonexistence of global solutions of degenerate and singular parabolic systems.
Existence and non-existence results for a nonlinear heat equation.
Existence and nonexistence results for reaction-diffusion equations in product of cones
Problems of existence and nonexistence of global nontrivial solutions to quasilinear evolution differential inequalities in a product of cones are investigated. The proofs of the nonexistence results are based on the test-function method developed, for the case of the whole space, by Mitidieri, Pohozaev, Tesei and Véron. The existence result is established using the method of supersolutions.
Existence and regularity for semilinear parabolic evolution equations
Existence and regularity of optimal solution for a dead oil isotherm problem.
Existence and stability of asymptotically oscillatory double pulses.
Existence and uniqueness for one-phase Stefan problems of nonclassical heat equations with temperature boundary condition at a fixed face.
Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems
A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution.
Existence and uniqueness of periodic solutions for a nonlinear reaction-diffusion problem.
We consider a class of degenerate reaction-diffusion equations on a bounded domain with nonlinear flux on the boundary. These problems arise in the mathematical modelling of flow through porous media. We prove, under appropriate hypothesis, the existence and uniqueness of the nonnegative weak periodic solution. To establish our result, we use the Schauder fixed point theorem and some regularizing arguments.