1,720,981 research outputs found
Contour enhancement via a singular free boundary problem
No full textWe study a degenerate nonlinear parabolic equation with moving
boundaries which describes the technique of contour enhancement in image
processing. Such problem arises from the model by Malladi and Sethian after
an asymptotic expansion suggested by Barenblatt: in order to recover the
phenomenon of mass concentration, a singular data is imposed at the free
boundary
Quasi-variational inequalities with Dirichlet boundary condition related to exit time problems for impulse control
No full textWe study degenerate-elliptic quasi-variational inequalities with Dirichlet boundary condition, which are related to the value function of the exit time problem for stochastic impulse control by means of the dynamic programming principle. The boundary condition in the viscosity solutions sense does not identify a unique solution, because in this nonlocal problem the boundary layer gives rise to a loss of information also at the interior points. The eventual discontinuities of solutions at the boundary of the domain play an essential role and cannot be removed. Therefore we superimpose a selection criterion which, enforcing the information coming from the boundary datum, picks up the value function among all possible viscosity solutions. As a result, we attain the continuity of the value function up to the boundary. In addition, we produce a monotone iterative scheme approximating the value function
Solution of Optimal Control Problems by Hybridization
No full textOptimization problems for hybrid systems have attracted a lot of attention in recent years. This interest stimulated numerous scientific works and the development of tools to study optimal trajectories, such as necessary conditions. The idea of the present contribution is to use such results for hybrid systems to construct a Hybridization of an optimal control problem. The approximation via a hybrid system was already considered in the literature, but using different methods. Our procedure gives an efficient approximation, i.e. in many cases more efficient than standard discretization. ©2005 IEEE
Singular free boundary problem from image processing
No full textWe study a degenerate nonlinear parabolic equation with moving boundaries which arises in the study of the technique of contour enhancement in image processing. In order to obtain mass concentration at the contour, singular data are imposed at the free boundary, leading to a nonstandard free boundary problem. Our main results are: (i) the well-posedness for the singular problem, without monotonicity assumptions on the initial datum, and (ii) the convergence of the approximation by means of combustion-type free-boundary problems
Bifurcation and symmetry breaking for the Hénon equation
No full textIn this paper we consider the Hénon problem in a ball. We prove the existence of (at least) one branch of nonradial solutions that bifurcate from the radial ones and that this branch is unbounded
Obstacle problem for nonlinear integro-differential equations arising in option pricing
No full textWe study the obstacle problem for a class of nonlinear integro-partial differential equations of second order, possibly degenerate, which includes the equation modeling American options in a jump-diffusion market with large investor. The viscosity solutions setting reveals appropriate, because of a monotonicity property with respect to the integral term. The same property allows to approximate the problem by penalization and to obtain the existence and uniqueness of solutions via a comparison principle. We also give uniform estimates of the solutions of the penalized problems which allow to prove further regularity
Uniqueness and comparison properties of the viscosity solution to some singular HJB equations
Full text linkWe study viscosity solutions to a class of HJB equations with singular coefficients near at the boundary: cases with either vanishing, or oscillating, or blowing-up diffusion coefficients are included. Because of proper structural conditions, strong comparison principle holds without assigning spatial boundary data, and unbounded initial data can be handled. The result applies to stochastic models for interest rate, and yields new results concerning Cauchy problems with unbounded coefficients
A One Dimensional Hyperbolic Model for Evolutionary Game Theory: Numerical Approximations and Simulations
No full textWe present a one space dimensional model with finite speed of propagation for population dynamics, based on a hyperbolic Cattaneo dynamics and evolutionary game theory. Comparison with parabolic models and numerical simulations are presented and discussed
A HYPERBOLIC MODEL OF SPATIAL EVOLUTIONARY GAME THEORY
No full textWe present a one space dimensional model with nite speed of
propagation for population dynamics, based both on the hyperbolic Cattaneo
dynamics and the evolutionary game theory. We prove analytical properties of
the model and global estimates for solutions, by using a hyperbolic nonlinear
Trotter product formula
Nonradial sign changing solutions to Lane–Emden problem in an annulus
No full textIn this paper we prove the existence of continua of nonradial solutions for the Lane–Emden equation in the annulus. In a first result we show that there are infinitely many global continua detaching from the curve of radial solutions with any prescribed number of nodal zones. Next, using the fixed point index in cone, we produce nonradial solutions with a new type of symmetry. This result also applies to solutions with fixed signed, showing that the set of solutions to the Lane–Emden problem has a very rich and complex structure
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