Zobrazeno 1 - 10
of 34
pro vyhledávání: '"Berg, Jan Bouwe van den"'
In the dynamics generated by the suspension bridge equation, traveling waves are an essential feature. The existing literature focuses primarily on the idealized one-dimensional case, while traveling structures in two spatial dimensions have only bee
Externí odkaz:
http://arxiv.org/abs/2405.19759
Integrating evolutionary partial differential equations (PDEs) is an essential ingredient for studying the dynamics of the solutions. Indeed, simulations are at the core of scientific computing, but their mathematical reliability is often difficult t
Externí odkaz:
http://arxiv.org/abs/2305.08221
Ground state solutions of elliptic problems have been analyzed extensively in the theory of partial differential equations, as they represent fundamental spatial patterns in many model equations. While the results for scalar equations, as well as cer
Externí odkaz:
http://arxiv.org/abs/2211.16445
To make progress towards better computability of Morse-Floer homology, and thus enhance the applicability of Floer theory, it is essential to have tools to determine the relative index of equilibria. Since even the existence of nontrivial stationary
Externí odkaz:
http://arxiv.org/abs/2206.09205
We use computer-assisted proof techniques to prove that a branch of non-trivial equilibrium solutions in the Kuramoto-Sivashinsky partial differential equation undergoes a Hopf bifurcation. Furthermore, we obtain an essentially constructive proof of
Externí odkaz:
http://arxiv.org/abs/2009.13597
In this paper we present a general approach to rigorously validate Hopf bifurcations as well as saddle-node bifurcations of periodic orbits in systems of ODEs. By a combination of analytic estimates and computer-assisted calculations, we follow solut
Externí odkaz:
http://arxiv.org/abs/2006.13373
This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our approximation, w
Externí odkaz:
http://arxiv.org/abs/2004.14830
In a previous paper we generalized the parameterization method of Cabr\'{e}, Fontich and De la Llave to center manifolds of discrete dynamical systems. In this paper, we extend this result to several different settings. The natural setting in which c
Externí odkaz:
http://arxiv.org/abs/2003.00701
Autor:
Berg, Jan Bouwe van den, Williams, JF
We consider the problem of rigorously computing periodic minimizers to the Ohta-Kawasaki energy. We develop a method to prove existence of solutions and determine rigorous bounds on the distance between our numerical approximations and the true infin
Externí odkaz:
http://arxiv.org/abs/1912.00059
In this paper we study travelling front solutions for nonlocal equations of the type \begin{equation} \partial_t u = N * S(u) + \nabla F(u), \qquad u(t,x) \in \mathbf{R}^d. \end{equation} Here $N *$ denotes a convolution-type operator in the spatial
Externí odkaz:
http://arxiv.org/abs/1907.03861