Fredholm property for a parameter dependent second order operator differential equation.
Fredholmness of an abstract differential equation of elliptic type.
Fredholmness of pseudo-differential operators with nonregular symbols
We establish the Fredholmness of a pseudo-differential operator whose symbol is of class , , in the spatial variable. Our work here refines the work of H. Abels, C. Pfeuffer (2020).
Free boundary eigenfunctions for a nonlinear degenerate eigenvalue problem.
Free boundary problem for the equations of magnetohydrodynamic incompressible viscous fluid
The existence of a global motion of magnetohydrodynamic fluid in a domain bounded by a free surface and under the external electrodynamic field is proved. The motion is such that the velocity and magnetic field are small in the H³-space.
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 arising in tumor models
We consider several simple models of tumor growth, described by systems of PDEs, and describe results on existence of solutions and on their asymptotic behavior. The boundary of the tumor region is a free boundary. In §1 the model assumes three types of cells, proliferating, quiescent and necrotic, and the corresponding PDE system consists of elliptic, parabolic and hyperbolic equations. The model in §2 assumes that the tumor has only proliferating cells. Finally in §3 we consider a model for treatment...
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...
Free boundary problems for nonstationary Navier-Stokes equations [Book]
Free boundary problems for Stoke's flows and finite element methods
Free boundary problems in fluid dynamics
Free Boundary Problems with Nonlinear Source Terms.
Free boundary regularity for harmonic measures and Poisson kernels.
Free boundary regularity in Stefan type problems
Regularity results of free boundaries for Stefan type problems are discussed. The influence that curvature may have on the behavior of the free boundary is studied and various open problems are also mentioned.
Free decay of solutions to wave equations on a curved background
We investigate for which metric (close to the standard metric ) the solutions of the corresponding d’Alembertian behave like free solutions of the standard wave equation. We give rather weak (i.e., non integrable) decay conditions on ; in particular, decays like along wave cones.
Free surface flow over an obstacle. Theoretical study of the fluvial case.
Free vibrations for the equation of a rectangular thin plate
In the paper, we deal with the equation of a rectangular thin plate with a simply supported boundary. The restoring force being an odd superlinear function of the vertical displacement, the existence of infinitely many nonzero time-periodic solutions is proved.
Free vibrations for the equation with sublinear
Free-energy-dissipative schemes for the Oldroyd-B model
In this article, we analyze the stability of various numerical schemes for differential models of viscoelastic fluids. More precisely, we consider the prototypical Oldroyd-B model, for which a free energy dissipation holds, and we show under which assumptions such a dissipation is also satisfied for the numerical scheme. Among the numerical schemes we analyze, we consider some discretizations based on the log-formulation of the Oldroyd-B system proposed by Fattal and Kupferman in [J. Non-Newtonian...
Frentes de explosión en ecuaciones de Hamilton Jacobi por argumentos de control determinista.