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We present an algorithm to approximate the solutions to variational problems where set of admissible functions consists of convex functions. The main motivator behind this numerical method is estimating solutions to Adverse Selection…

Optimization and Control · Mathematics 2008-03-07 Ivar Ekeland , Santiago Moreno

In this paper, we address the problem of existence and uniqueness of a global classical solution to a multidimensional stochastic Burgers equation without gradient-type assumptions on the force or the initial condition. The equation is…

Probability · Mathematics 2019-04-22 Alberto Ohashi , Evelina Shamarova

The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…

Classical Analysis and ODEs · Mathematics 2025-01-09 Alberto Lastra

We establish that the initial value problem for a generalised Burgers equation considered in part I of this paper, is well-posed. We also establish several qualitative properties of solutions to the initial value problem utilised in part I…

Analysis of PDEs · Mathematics 2022-09-13 John Christopher Meyer , David John Needham

The Einstein field equations, or generalizations thereof, are difficult to solve analytically. On the other hand, numerical solutions of the same equations have become increasingly common, in particular concerning compact objects. Whereas…

General Relativity and Quantum Cosmology · Physics 2024-10-01 Jianzhi Yang , Pedro V. P. Cunha , Carlos A. R. Herdeiro

We prove the existence and uniqueness of a classical solution to a multidimensional non-potential stochastic Burgers equation with H\"older continuous initial data. Our motivation is the adhesion model in the theory of formation of the…

Analysis of PDEs · Mathematics 2019-11-13 Yuri Gliklikh , Evelina Shamarova

The solution of the problem on reduction operators and nonclassical reductions of the Burgers equation is systematically treated and completed. A new proof of the theorem on the special "no-go" case of regular reduction operators is…

Mathematical Physics · Physics 2013-01-15 Oleksandr A. Pocheketa , Roman O. Popovych

Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…

Classical Analysis and ODEs · Mathematics 2021-03-02 T. M. Dunster

We consider an inverse problem for the linear one-dimensional wave equation with variable coefficients consisting in determining an unknown source term from a boundary observation. A method to obtain approximations of this inverse problem…

Numerical Analysis · Mathematics 2025-01-22 Carlos Castro , Sorin Micu

In this article we establish strong convergence rates on the whole probability space for explicit full-discrete approximations of stochastic Burgers equations with multiplicative trace-class noise. The key step in our proof is to establish…

Probability · Mathematics 2022-11-01 Martin Hutzenthaler , Robert Link

The coupled Burgers equation is solved by way of the trigonometric B-spline collocation method. The unknown of the coupled Burgers equation is integrated in time by aid of the Crank-Nicolson method. Resulting time-integrated coupled Burgers…

Numerical Analysis · Mathematics 2016-04-18 Ozlem Ersoy , Idris Dag

We study the problem of global exponential stabilization of original Burgers' equations and the Burgers' equation with nonlocal nonlinearities by controllers depending on finitely many parameters. It is shown that solutions of the…

Analysis of PDEs · Mathematics 2019-12-13 Serap Gumus , Varga K. Kalantarov

Analytic continuation of viscous shock solution for the generalized Burgers equation with polynomial nonlinear source term is investigated. We show that a pertubated wave recovers its analyticity in the space variable in the strip limited…

Analysis of PDEs · Mathematics 2008-12-18 Cédric Lejard

An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…

Numerical Analysis · Mathematics 2015-10-29 Petr N. Vabishchevich

The conformable double ARA decomposition approach is presented in this current study to solve one-dimensional regular and singular conformable functional Burger's equations. We investigate the conformable double ARA transform's definition,…

General Mathematics · Mathematics 2023-06-21 Amjad E. Hamza , Abdelilah K. Sedeeg , Rania Saadeh , Ahmad Qazza , Raed Khalil

We present a strategy for interpreting nonlinear, characteristic-type penalty terms as numerical boundary flux functions that provide provable bounds for solutions to nonlinear hyperbolic initial boundary value problems with open…

Numerical Analysis · Mathematics 2026-03-04 Andrew R. Winters , David A. Kopriva , Jan Nordström

Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium with a power law spatial density profile, are presented. The solutions are a generalization of the well known…

Fluid Dynamics · Physics 2021-06-02 Menahem Krief

We derive a-priori error estimates for the finite-element approximation of a distributed optimal control problem governed by the steady one-dimensional Burgers equation with pointwise box constraints on the control. Here the approximation…

Optimization and Control · Mathematics 2014-11-18 Pedro Martín Merino Rosero

In this paper, we consider Burgers' equation with uncertain boundary and initial conditions. The polynomial chaos (PC) approach yields a hyperbolic system of deterministic equations, which can be solved by several numerical methods. Here,…

Numerical Analysis · Mathematics 2019-02-04 Philipp Öffner , Jan Glaubitz , Hendrik Ranocha

We study admissible transformations and Lie symmetries for a class of variable-coefficient Burgers equations. We combine the advanced methods of splitting into normalized subclasses and of mappings between classes that are generated by…

Mathematical Physics · Physics 2020-05-19 Stanislav Opanasenko , Alexander Bihlo , Roman O. Popovych