Related papers: On the Initial Value Problem for Causal Variationa…
Initial-boundary value problems in a half-strip with different types of boundary conditions for two-dimensional Zakharov-Kuznetsov equation are considered. Results on global existence, uniqueness and long-time decay of weak and regular…
In this contribution we develop a solution theory for singular quasilinear stochastic partial differential equations subject to an initial condition. We obtain our solution theory as a perturbation of the rough path approach developed to…
We establish three variational principles for the upper metric mean dimension with potential of level sets of continuous maps in terms of the entropy of partitions and Katok's entropy of the underlying system. Our results hold for dynamical…
This paper develops some mathematical models arising in behavioral sciences, particularly in psychology, which are formalized via general preferences with variable ordering structures. Our considerations are based on the recent variational…
Causal spaces have recently been introduced as a measure-theoretic framework to encode the notion of causality. While it has some advantages over established frameworks, such as structural causal models, the theory is so far only developed…
We consider the initial boundary value problem for a model system of one-dimensional equations which describe unsteady polytropic motions of a mixture of viscous compressible fluids. We prove the global existence and uniqueness theorem for…
A new method is introduced for studying boundary value problems for a class of linear PDEs with {\it variable} coefficients. This method is based on ideas recently introduced by the author for the study of boundary value problems for PDEs…
We present the variational action principle for initial value problems in classical, conservative-force point particle mechanics. We rigorously derive this formulation by taking the classical limit of the Schwinger-Keldysh expression for…
The goal of this work is to discuss how should we impose initial values in fractional problems to ensure that they have exactly one smooth unique solution, where smooth simply means that the solution lies in a certain suitable space of…
This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these…
A key issue in dimension reduction of dissipative dynamical systems with spectral gaps is the identification of slow invariant manifolds. We present theoretical and numerical results for a variational approach to the problem of computing…
We present a stable and convergent method for solving initial value problems based on the use of differentiation matrices obtained by Lagrange interpolation. This implicit multistep-like method is easy-to-use and performs pretty well in the…
Based on the principle of causality, I advance a new principle of variation and try to use it as the most general principle for research into laws of nature.
We introduce the most general class of linear boundary-value problems for systems of first-order ordinary differential equations whose solutions belong to the complex H\"older space $C^{n+1,\alpha}$, with $0\leq n\in\mathbb{Z}$ and…
This work develops problem statements related to encoders and autoencoders with the goal of elucidating variational formulations and establishing clear connections to information-theoretic concepts. Specifically, four problems with varying…
We derive the Euler-Lagrange equations for minimizers of causal variational principles in the non-compact setting with constraints, possibly prescribing symmetries. Considering first variations, we show that the minimizing measure is…
We investigate an initial-(periodic-)boundary value problem for a continuum equation, which is a model for motion of grain boundaries based on the underlying microscopic mechanisms of line defects (disconnections) and integrated the effects…
We study the initial-boundary value problem of the stochastic Navier--Stokes equations in the half space. We prove the existence of weak solutions in the standard Besov space valued random processes when the initial data belong to the…
The initial value problem is well-defined on a class of spacetimes broader than the globally hyperbolic geometries for which existence and uniqueness theorems are traditionally proved. Simple examples are the time-nonorientable spacetimes…
This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite…