Related papers: A heat equation approach to intertwining
We present a novel, generalised formulation to treat coupled structural integrity problems by combining phase field and multi-physics modelling. The approach exploits the versatility of the heat transfer equation and is therefore well…
This paper investigates the numerical modeling of a time-dependent heat transmission problem by the convolution quadrature boundary element method. It introduces the latest theoretical development into the error analysis of the numerical…
This paper surveys hyperinterpolation, a quadrature-based approximation scheme. We cover classical results, provide examples on several domains, review recent progress on relaxed quadrature exactness, introduce methodological variants, and…
We derive a matrix version of Li \& Yau--type estimates for positive solutions of semilinear heat equations on Riemannian manifolds with nonnegative sectional curvatures and parallel Ricci tensor, similarly to what R.~Hamilton did…
The article provides a pedagogical review aimed at graduate students in materials science, physics, and applied mathematics, focusing on recent developments in the subject. Following a brief summary of concepts from complex analysis, the…
A solution of the heat equation with a distribution-valued potential is constructed by regularization. When the potential is the generalized derivative of a H\"{o}lder continuous function, regularity of the resulting solution is in line…
The paper aims to propose a suitable method in finding the solution of tensor complementarity problem. The tensor complementarity problem is a subclass of nonlinear complementarity problems for which the involved function is defined by a…
In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In…
Recently, a new fractional derivative called the conformable fractional derivative is given which is based on the basic limit definition of the derivative in [1]. Then, the fractional versions of chain rules, exponential functions,…
A proof of the monotonicity of an entropy like energy for the heat equation on a quaternionic contact and CR manifolds is proven
We present a fluctuation relation for heat dissipation in a nonequilibrium system. A nonequilibrium work is known to obey the fluctuation theorem in any time interval $t$. A heat, which differs from a work by an energy change, is shown to…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
The aim of the present paper is to give extensions of the cosine-sine functional equation.
This article is a survey of recent developments in, and a tutorial on, the approach to P v. NP and related questions called Geometric Complexity Theory (GCT). It is written to be accessible to graduate students. Numerous open questions in…
Transformation optics originating from the invariance of Maxwell's equations under the coordinate mapping has enabled the design and demonstration of many fascinating electromagnetic devices that were unconceivable or deemed impossible…
A construction of differential constraints compatible with partial differential equations is considered. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the classical…
We use reproducing kernel methods to study various rigidity problems. The methods and setting allow us to also consider the non-positive case.
In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…
Thermal diffusivity measurements of samples transmitting thermal radiation require adjustments to the data treatment procedures in laser flash analysis. Conventionally, an unconstrained diathermic model is used. Current results show that…
We study the Radiative Transfer equations coupled with the time dependent temperature equation of a fluid: existence, uniqueness, a maximum principle are established. A short numerical section illustrates the pros and cons of the method.