Related papers: Higher order linear parabolic equations
We study a higher order parabolic partial differential equation that arises in the context of condensed matter physics. It is a fourth order semilinear equation whose nonlinearity is the determinant of the Hessian matrix of the solution. We…
We highlight a striking difference in behavior between two widely used variants of coordinate ascent variational inference: the sequential and parallel algorithms. While such differences were known in the numerical analysis literature in…
For a class of nonlinear hyperbolic systems of second order the paper shows that all Lax modes associated with their first-order formulations are linearly degenerate. This property holds for recently considered models of dissipative…
Differential equations with the Painlev\'e property have been studied extensively due to their appearance in many branches of mathematics and their applicability in physics. Although a modern, differential algebraic treatment of the order…
Second-order two-scale expansions, a unified proof for the regularity of the correctors based on the translation invariant and a lemma for extracting $O(\epsilon)$ from the remainder term are presented for the second order nonlinear…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
A class of second-order differential equations commonly arising in physics applications are considered, and their explicit hypergeometric solutions are provided. Further, the relationship with the Generalized and Universal Associated…
We study a class of degenerate parabolic and elliptic equations in divergence form in the upper half space $\{x_d>0\}$. The leading coefficients are of the form $x_d^2a_{ij}$, where $a_{ij}$ are bounded, uniformly elliptic, and measurable…
We study a scalar hyperbolic partial differential equation with non-linear terms similar to those of the equations of general relativity. The equation has a number of non-trivial analytical solutions whose existence rely on a delicate…
This paper is concerned with quantitative homogenization of second-order parabolic systems with periodic coefficients varying rapidly in space and time, in different scales. We obtain large-scale interior and boundary Lipschitz estimates as…
The motion of binary star systems is re-examined in the presence of perturbations from the theory of general relativity. The Kepler problem is regularized and linearized with quaternions. In this way first order perturbation results are…
A third order parabolic operator L_\epsilon typical of a non linear wave operator cal L_0 perturbed by viscous terms, is analyzed. Some particular solutions related to L_0 are explicitly determined and the initial value problem for…
The dynamics of the second order rational difference equation $\displaystyle{z_{n+1}=\frac{\alpha + z_{n-1}}{\beta z_n + z_{n-1}}}$ with the real parameter $\alpha$, $\beta$ and arbitrary non-negative real initial conditions is investigated…
We consider the size of the nodal set of the solution of the second order parabolic-type equation with Gevrey regular coefficients. We provide an upper bound as a function of time. The dependence agrees with a sharp upper bound when the…
This work is devoted to the strong unique continuation problem for second order parabolic equations with nonsmooth coefficients. Introduction and bibliography have been revised.
In this paper, we study a new model of nonlocal geometric equations which appears in tomographic reconstruction when using the level-set method. We treat two additional difficulties which make the work original. On one hand, the level lines…
We establish a consistency result by comparing two independent notions of generalised solutions to a large class of linear hyperbolic first order PDE systems with constant coefficients, showing that they eventually coincide. The first is…
Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…
We distinguish two extreme classes of perturbation problems depending on the signs of second-order energy corrections and argue why it is generally much more probable to obtain a negative value of the same for any state in the standard…
Motivated by important applications in image processing, we study a class of second-order geometric quasilinear hyperbolic partial differential equations (PDEs). This is inspired by the recent development of second-order damping systems…