Related papers: On the trace embedding and its applications to evo…
Many innovative applications require establishing correspondences among 3D geometric objects. However, the countless possible deformations of smooth surfaces make shape matching a challenging task. Finding an embedding to represent the…
It is known that solutions of nonlocal dispersal evolution equations do not become smoother in space as time elapses. This lack of space regularity would cause a lot of difficulties in studying transition fronts in nonlocal equations. In…
Stability and convergence of full discretizations of various surface evolution equations are studied in this paper. The proposed discretization combines a higher-order evolving-surface finite element method (ESFEM) for space discretization…
Obstacles to integrability in perturbed evolution equations are overcome by allowing higher-order terms in the expansion of the solution to depend explicitly on time and position. With a special expansion algorithm, obstacles vanish…
We discuss the issue of maximal regularity for evolutionary equations with non-autonomous coefficients. Here evolutionary equations are abstract partial-differential algebraic equations considered in Hilbert spaces. The catch is to consider…
We review some results on the logarithmic convexity for evolution equations, a well-known method in inverse and ill-posed problems. We start with the classical case of self-adjoint operators. Then, we analyze the case of analytic…
Given $E_0, E_1, F_0, F_1, E$ rearrangement invariant function spaces, $a_0$, $a_1$, $b_0$, $b_1$, $b$ slowly varying functions and $0< \theta_0<\theta_1<1$, we characterize the interpolation spaces $$(\overline{X}^{\mathcal…
This work is focused on the application of functional-type a posteriori error estimates and corresponding indicators to a class of time-dependent problems. We consider the algorithmic part of their derivation and implementation and also…
Trace conjunction integrals are introduced and studied. They appear in trace conjunction inequalities which unify the Hardy inequality on a halfspace and the classical Gagliardo trace inequality. At the endpoint they satisfy a…
Functional evolution equations are used in the modeling of numerous physical processes. In this work, our main tool is perturbation theory of strongly continuous semigroups. The advantage of this technique is that one can provide functional…
We introduce a general approach to traces that we consider as linear continuous functionals on some function space where we focus on some special choices for that space. This leads to an integral calculus for the computation of the precise…
Evolutionary algorithms have been frequently used for dynamic optimization problems. With this paper, we contribute to the theoretical understanding of this research area. We present the first computational complexity analysis of…
We introduce the notion of coupled embeddability, defined for maps on products of topological spaces. We use known results for nonsingular biskew and bilinear maps to generate simple examples and nonexamples of coupled embeddings. We study…
We study geometric properties of trace functionals that generalize those in [Zhang, Adv. Math. 365:107053 (2020)], arising from a novel family of conditional entropies with applications in quantum information. Building on new convexity…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…
The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
Using the Carleman linearization technique the continuous iteration of a mapping is studied. Based on the detailed analysis of the Carleman embedding matrix the precise mathematical meaning is given to such notion. The ordinary differential…
We prove a compactness result related to $G$-convergence for autonomous evolutionary equations in the sense of Picard. Compared to previous work related to applications, we do not require any boundedness or regularity of the underlying…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…