Related papers: The heat-balance integral method by a parabolic pr…
We prove the parabolic boundary Harnack inequality in parabolic flat Lipschitz domains by blow-up techniques, allowing for the first time a non-zero right-hand side. Our method allows us to treat solutions to equations driven by…
We investigate the large-time behavior of the sign-changing solution of the inhomogeneous semilinear heat equation with a forcing term depending of time and space. we identify the critical exponent for this problem, which separates the…
The standard problem for the classical heat equation posed in a bounded domain $\Omega$ of $\mathbb R^n$ is the initial and boundary value problem. If the Laplace operator is replaced by a version of the fractional Laplacian, the initial…
We study the ultimate bounds on the estimation of temperature for an interacting quantum system. We consider two coupled bosonic modes that are assumed to be thermal and using quantum estimation theory establish the role the Hamiltonian…
An analytic solution to a stationary heat conduction problem in 2D unbounded doubly periodic composite materials with temperature dependent conductivities of their components is given. Corresponding nonlinear boundary value problem is…
We study the well-posedness of the compressible boundary layer equations with data being analytic in the tangential variable of the boundary. The compressible boundary layer equations, a nonlinear coupled system of degenerate parabolic…
An important challenge when coupling two different time dependent problems is to increase parallelization in time. We suggest a multirate Neumann-Neumann waveform relaxation algorithm to solve two heterogeneous coupled heat equations. In…
We present a waveform relaxation version of the Dirichlet-Neumann and Neumann-Neumann methods for parabolic problems. Like the Dirichlet-Neumann method for steady problems, the method is based on a non-overlapping spatial domain…
This paper focuses on parabolic final value problems, and well-posedness is proved for a large class of these. The clarification is obtained from Hilbert spaces that characterise data that give existence, uniqueness and stability of the…
We consider piecewise polynomial discontinuous Galerkin discretizations of boundary integral reformulations of the heat equation. The resulting linear systems are dense and block-lower triangular and hence can be solved by block forward…
We consider initial-boundary value problems (IBVPs) on a finite interval for the system of the energy balance equation and Guyer-Krumhansl constitutive equation. Boundary conditions comprise various models of behavior of a physical system…
Understanding the generation mechanism of the heating flux is essential for the design of hypersonic vehicles. We proposed a novel formula to decompose the heat flux coefficient into the contributions of different terms by integrating the…
In a domain of the Euclidean space, we estimate from below the distance to the boundary of global maximum points of solutions of elliptic and parabolic equations with homogeneous Dirichlet boundary values. As reference cases, we first…
Here a mixed problem for a nonlinear hyperbolic equation with Neumann boundary value condition is investigated, and a priori estimations for the possible solutions of the considered problem are obtained. These results demonstrate that any…
This paper deals with the numerical methods for the reconstruction of source term in linear parabolic equation from final overdetermination. We assume that the source term has the form f(x)h(t) and h(t) is given, which guarantees the…
In bounded $n$-dimensonal domains with $n\ge 1$, this manuscript examines an initial-boundary value problem for the system \[ \left\{ \begin{array}{l} u_{tt} = \nabla \cdot (\gamma(\Theta) \nabla u_t) + a \nabla \cdot (\gamma(\Theta) \nabla…
This manuscript deals with the analysis of numerical methods for the full discretization (in time and space) of the linear heat equation with Neumann boundary conditions, and it provides the reader with error estimates that are uniform in…
We consider the one-dimensional heat and wave equations but -- instead of boundary conditions-- we impose on the solution certain non-local, integral constraints. An appropriate Hilbert setting leads to an integration-by-parts formula in…
The aim of this article is to show how certain parabolic theorems follow from their elliptic counterparts. This technique is demonstrated through new proofs of five important theorems in parabolic unique continuation and the regularity…
We study the diffusion (or heat) equation on a finite 1-dimensional spatial domain, but we replace one of the boundary conditions with a "nonlocal condition", through which we specify a weighted average of the solution over the spatial…