相关论文: Quasilinearization Approach to Nonlinear Problems …

New problem is studied that is to find nonlinear differential equations with special solutions expressed via the Weierstrass function. Method is discussed to construct nonlinear ordinary differential equations with exact solutions. Main…

We present an efficient quantum algorithm to simulate nonlinear differential equations with polynomial vector fields of arbitrary degree on quantum platforms. Models of physical systems that are governed by ordinary differential equations…

The existence of a formal particular solution (family of solutions) of oscillating type under certain conditions has been proved for the quasi-linear ordinary differential equations system. The asymptotic nature of this solution (the family…

New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…

We consider singular solutions to quasilinear elliptic equations under zero Dirichlet boundary condition. Under suitable assumptions on the nonlinearity we deduce symmetry and monotonicity properties of positive solutions via an improved…

We review a recent generalization of Normal Form Theory to systems (Hamiltonian ones or general ODEs) where the perturbing term is not periodic in one coordinate variable. The main difference with the standard case relies on the non…

For the system of second order quasilinear parabolic equations the problem of reducing them to the equations of diffusion type is considered. In non-degenerate case an effective algorithm for solving this problem is suggested.

Quantum algorithms offer an exponential advantage with respect to the number of dependent variables for solving certain nonlinear ordinary differential equations (ODEs). These algorithms typically begin by transforming the original…

Quadratization of polynomial and nonpolynomial systems of ordinary differential equations is advantageous in a variety of disciplines, such as systems theory, fluid mechanics, chemical reaction modeling and mathematical analysis. A…

In this paper, we provide a direct approach to the existence and uniqueness of strong (in the probabilistic sense) and weak (in the PDE sense) solutions to quasilinear stochastic partial differential equations, which are neither monotone…

We consider several models (including both multidimensional ordinary differential equations (ODEs) and partial differential equations (PDEs), possibly ill-posed), subject to very strong damping and quasi-periodic external forcing. We study…

We prove linear convergence for a new family of modified Dirichlet--Neumann methods applied to quasilinear parabolic equations, as well as the convergence of the Robin--Robin method. Such nonoverlapping domain decomposition methods are…

This contribution, built on the companion paper [1], is focused on the different mathematical approaches available for the analysis of the quasilinear approximation in plasma physics.

We prove the existence and uniqueness of solution of quasilinear stochastic partial differential equations with obstacle (OSPDEs in short) in degenerate case. Using De Giorgi's iteration, we deduce the $L^p-$estimates for the time-space…

In this paper, we establish a relation between two seemingly unrelated concepts for solving first-order hyperbolic quasilinear systems of partial differential equations in many dimensions. These concepts are based on a variant of the…

Aim of this work is the study of differential equations governing non--dissipative non--linear oscillators; these arise in different physical models such as the treatment of relativistic oscillators, up to generalizations to Duffing's…

Some of recent developments, including recent results, ideas, techniques, and approaches, in the study of degenerate partial differential equations are surveyed and analyzed. Several examples of nonlinear degenerate, even mixed, partial…

We consider a quasilinear elliptic equation involving a first order term, under zero Dirichlet boundary condition in half spaces. We prove that any positive solution is monotone increasing w.r.t. the direction orthogonal to the boundary.…

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…

We show that the virial theorem provides a useful simple tool for approximating nonlinear problems. In particular we consider conservative nonlinear oscillators and a bifurcation problem. In the former case we obtain the same main result…