Entropy solutions to a second order forward-backward parabolic differential equation.
Error estimates for Stokes problem with Tresca friction conditions
In this paper, we present and study a mixed variational method in order to approximate, with the finite element method, a Stokes problem with Tresca friction boundary conditions. These non-linear boundary conditions arise in the modeling of mold filling process by polymer melt, which can slip on a solid wall. The mixed formulation is based on a dualization of the non-differentiable term which define the slip conditions. Existence and uniqueness of both continuous and discrete solutions of these...
Existence of a principal eigenvalue for the Tricomi problem.
Existence of solutions for a nonlinear hyperbolic-parabolic equation in a non-cylinder domain.
Existenz und Eindeutigkeit für Lösungen des Neumann-Tricomi-Problems im ...
Finite Element Variational Crimes in Parabolic-Elliptic Problems. Part I. Nonlinear Schemes.
Free boundary problems and transonic shocks for the Euler equations in unbounded domains
We establish the existence and stability of multidimensional transonic shocks (hyperbolic-elliptic shocks), which are not nearly orthogonal to the flow direction, for the Euler equations for steady compressible potential fluids in unbounded domains in . The Euler equations can be written as a second order nonlinear equation of mixed hyperbolic-elliptic type for the velocity potential. The transonic shock problem can be formulated into the following free boundary problem: The free boundary is the...
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...
Gevrey problem for parabolic equations with changing time direction.
Global Existence and Boundedness of Solutions to a Model of Chemotaxis
A model of chemotaxis is analyzed that prevents blow-up of solutions. The model consists of a system of nonlinear partial differential equations for the spatial population density of a species and the spatial concentration of a chemoattractant in n-dimensional space. We prove the existence of solutions, which exist globally, and are L∞-bounded on finite time intervals. The hypotheses require nonlocal conditions on the species-induced production of the chemoattractant.
Global existence and decay estimate of solution for Cahn-Hilliard equation with inertial term
The Cauchy problem of the Cahn-Hilliard equation with inertial term in multi space dimension is considered. Based on detailed analysis of Green’s function, using fixed-point theorem, we get the global existence in time of classical solution with large initial data. Furthermore, we get decay rate of the solution.
Global solutions for a problem modeling the dynamics of a system of self-gravitating Brownian particles
Results on the global existence and uniqueness of variational solutions to an elliptic-parabolic problem occurring in statistical mechanics are provided.
Global solutions to vortex density equations arising from sup-conductivity
High-order mixed-type differential equations with weighted integral boundary conditions.
Initial boundary value problem for generalized Zakharov equations
This paper considers the existence and uniqueness of the solution to the initial boundary value problem for a class of generalized Zakharov equations in dimensions, and proves the global existence of the solution to the problem by a priori integral estimates and the Galerkin method.
Initial-boundary value problems for quasilinear dispersive equations posed on a bounded interval.
-оценки решений общих краевых задач для уравнения со смешанной парабoло-эллиптической структурой
Le problème mixte des équations des ondes et applications
Linear scheme for finite element solution of nonlinear parabolic-elliptic problems with nonhomogeneous Dirichlet boundary condition
The computation of nonlinear quasistationary two-dimensional magnetic fields leads to a nonlinear second order parabolic-elliptic initial-boundary value problem. Such a problem with a nonhomogeneous Dirichlet boundary condition on a part of the boundary is studied in this paper. The problem is discretized in space by the finite element method with linear functions on triangular elements and in time by the implicit-explicit method (the left-hand side by the implicit Euler method and the right-hand...
Local solvability of degenerate Monge-Ampère equations and applications to geometry.