Related papers: Solving Obstacle Problems using Optimal Homotopy A…
We consider the obstacle problem with two irregular reflecting barriers for the Cauchy-Dirichlet problem for semilinear parabolic equations with measure data. We prove the existence and uniqueness of renormalized solutions of the problem…
New computational strategies, such as molecular docking, are emerging to speed up the drug discovery process. This method predicts the activity of molecules at the binding site of proteins, helping to select the ones that exhibit desirable…
Nonlinear programming (NLP) plays a critical role in domains such as power energy systems, chemical engineering, communication networks, and financial engineering. However, solving large-scale, nonconvex NLP problems remains a significant…
We analyze Riemannian Hamiltonian Monte Carlo (RHMC) for sampling a polytope defined by $m$ inequalities in $\R^n$ endowed with the metric defined by the Hessian of a convex barrier function. The advantage of RHMC over Euclidean methods…
For nonlinear equations, the homotopy methods (continuation methods) are popular in engineering fields since their convergence regions are large and they are quite reliable to find a solution. The disadvantage of the classical homotopy…
Variational problems under uniform quasiconvex constraints on the gradient are studied. In particular, existence of solutions to such problems is proved as well as existence of lagrange multipliers associated to the uniform constraint. They…
In the paper, we consider the obstacle problem, with one and two irregular barriers, for semilinear evolution equation involving measure data and operator corresponding to a semi-Dirichlet form. We prove the existence and uniqueness of…
The steady motion of a viscous incompressible fluid in a multiply-connected, planar, bounded domain (perforated with a large number of small holes) is modeled through the Navier-Stokes equations with non-homogeneous Dirichlet boundary data…
Avoiding hybrid obstacles in unknown scenarios with an efficient flight strategy is a key challenge for unmanned aerial vehicle applications. In this paper, we introduce a more robust technique to distinguish and track dynamic obstacles…
In optimization the duality gap between the primal and the dual problems is a measure of the suboptimality of any primal-dual point. In classical mechanics the equations of motion of a system can be derived from the Hamiltonian function,…
We use a characterization of the fractional Laplacian as a Dirichlet to Neumann operator for an appropriate differential equation to study its obstacle problem in perforated domains.
This work investigates the application of the Newton's method for the numerical solution of a nonlinear boundary value problem formulated through an ordinary differential equation (ODE). Nonlinear ODEs arise in various mathematical modeling…
Existence of stationary solutions to a nonlocal fourth-order elliptic obstacle problem arising from the modelling of microelectromechanical systems with heterogeneous dielectric properties is shown. The underlying variational structure of…
Lie symmetry method is applied to find analytic solutions of initial-boundary-value problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a…
In this paper, we deal with an elliptic problem with the Dirichlet boundary condition. We operate in Sobolev spaces and the main analytic tool we use is the Lax-Milgram lemma. First, we present the variational approach of the problem which…
A formulation of the boundary integral method for solving partial differential equations has been developed whereby the usual weakly singular integral and the Cauchy principal value integral can be removed analytically. The broad…
We study the obstacle problem for the Evolutionary p-Laplace Equation when the obstacle is discontinuous and without regularity in the time variable. Two quite different procedures yield the same solution.
This paper presents a numerical approach to the stochastic obstacle problem using the stochastic Galerkin (SG) method. Due to the low regularity of the solution, linear finite elements are employed in both the physical and random variable…
This work is devoted to studying dynamic interpolation for obstacle avoidance. This is a problem that consists of minimizing a suitable energy functional among a set of admissible curves subject to some interpolation conditions. The given…
We introduce a new constructive method for establishing lower bounds on convergence rates of periodic homogenization problems associated with divergence type elliptic operators. The construction is applied in two settings. First, we show…