Related papers: Computability of Initial Value Problems

A backdoor in a finite-domain CSP instance is a set of variables where each possible instantiation moves the instance into a polynomial-time solvable class. Backdoors have found many applications in artificial intelligence and elsewhere,…

This article considers the spatially inhomogeneous, non-cutoff Boltzmann equation. We construct a large-data classical solution given bounded, measurable initial data with uniform polynomial decay of mild order in the velocity variable. Our…

Using a recent result of C. De Lellis and L. Sz\'{e}kelyhidi Jr. we show that, in the case of periodic boundary conditions and for dimension greater or equal 2, there exist infinitely many global weak solutions to the incompressible Euler…

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…

We consider the Cauchy problem for the nonlinear Schr\"odinger equation on the whole space. After introducing a weaker concept of finite speed of propagation, we show that the concatenation of initial data gives rise to solutions whose time…

A slightly modified variant of the cubic periodic one-dimensional nonlinear Schroedinger equation is shown to admit weak solutions for all initial data in certain function spaces wider than L^2. These solutions depend uniformly continuously…

As one of the seven open problems in the addendum to their 1989 book "Computability in Analysis and Physics", Pour-El and Richards proposed ``... the recursion theoretic study of particular nonlinear problems of classical importance.…

Quantum algorithms and complexity have recently been studied not only for discrete, but also for some numerical problems. Most attention has been paid so far to the integration problem, for which a speed-up is shown by quantum computers…

We study the existence of a strong solution to the initial value problem for the incompressible Navier-Stokes equations in the whole space. Our investigation shows that a ``suitable'' weak solution to the problem becomes a strong one…

We consider the classical initial and boundary value problem for the Cahn--Hilliard equation with non-degenerate mobility and singular (e.g., logarithmic) potential. We prove that any weak solution converges to a single equilibrium using…

We consider initial boundary value problems with the homogeneous Neumann boundary condition. Given an initial value, we establish the uniqueness in determining a spatially varying coefficient of zeroth-order term by a single measurement of…

A new method for solving stiff boundary value problems is described and compared to other known approaches using the Troesch's problem as a test example. The method is based on the general idea of alternate approximation of either the…

We establish the global existence of weak solutions to a nonlinear kinetic Fokker--Planck equation with degenerate diffusion, under either inflow or partial absorption-reflection boundary conditions. The novelty of our approach lies in…

This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…

It is shown that a strong solution of the Camassa-Holm equation, initially decaying exponentially together with its spacial derivative, must be identically equal to zero if it also decays exponentially at a later time. In particular, a…

We axiomatize and generalize Markov's approach to the continuity problem for Type 1 computable functions, i.e. the problem of finding sufficient conditions on a computable topological space to obtain a theorem of the form "computable…

We consider the time dependent Schrodinger equation on a complex semi-simple Lie group. We consider initial data a bi-invariant function. We prove that if the initial data decays fast enough, and the solution decays fast enough at one time…

We establish two complementary results about the regularity of the solution of the periodic initial value problem for the linear Benjamin-Ono equation. We first give a new simple proof of the statement that, for a dense countable set of the…

In this work, we investigate the IVP for a time-fractional fourth-order equation with nonlinear source terms. More specifically, we consider the time-fractional biharmonic with exponential nonlinearity and the time-fractional Cahn-Hilliard…

We show in Bishop's constructive mathematics---in particular, using countable choice---that weak K\"{o}nig's lemma implies the uniform continuity theorem.