相关论文: Sets of unique continuation for heat equation
We explicate a procedure to solve general linear differential equations, which connects the desired solutions to monomials x^m of an appropriate degree m. In the process the underlying symmetry of the equations under study, as well as that…
The present paper deals with the existence and uniqueness of global classical solutions to the continuous coagulation and nonlinear multiple fragmentation equations for large classes of unbounded coagulation, collision and breakup kernels.…
A class of models of heat transfer processes in a multilayer domain is considered. The governing equation is a nonlinear heat-transfer equation with different temperature-dependent densities and thermal coefficients in each layer.…
We establish a connection between a sharp double-sided Harnack bound for positive solutions of a fractional heat equation and the circular geometry in higher dimensions. The present work extends and generalizes the results obtained in the…
In this paper, we study the structure and dynamical properties of protein contact networks with respect to other biological networks, together with simulated archetypal models acting as probes. We consider both classical topological…
Adaptive methods for derivation of analytical and numerical solutions of heat diffusion in one dimensional thin rod have investigated. Comperhensive comparsion analysis based on the homotopy perturbation method (HPM) and finite difference…
We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that…
This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…
Evolutionary PDEs for geometric order parameters that admit propagating singular solutions are introduced and discussed. These singular solutions arise as a result of the competition between nonlinear and nonlocal processes in various…
We show that it is possible to construct microscopic-level discrete equations from macroscopic modeling PDEs for heat conduction in one space dimension. The significance of this result is that, in general, one starts from microscopic…
In gas dynamics, the connection between the continuum physics model offered by the Navier-Stokes equations and the heat equation and the molecular model offered by the kinetic theory of gases has been understood for some time, especially…
We derive an explicit representation of the fundamental solution to the heat equation in a half-space of ${\mathbb R}^N$ with a diffusive dynamical boundary condition, and establish sharp pointwise upper and lower bounds. We also…
In this research paper, we provide a concise overview of fractal calculus applied to fractal sets. We introduce and solve a second $\alpha$-order fractal differential equation with constant coefficients across different scenarios. We…
A solution to the heat equation between Riemannian manifolds, where the domain is compact and possibly has boundary, will not leave a compact and locally convex set before the image of the boundary does.
We show that a large class of stochastic heat equations can be approximated by systems of interacting stochastic differential equations. As a consequence, we prove various comparison principles extending earlier results. Among other things,…
Rapid processes of heat transfer are not described by the standard heat conduction equation. To take into account a finite velocity of heat transfer, we use the hyperbolic model of heat conduction, which is connected with the relaxation of…
We prove a theorem of unique continuation in measure for nonlocal equations of the type $(\partial_t - \Delta)^s u= V(x,t) u$, for $0<s <1$. Our main result, Theorem 1.1, establishes a delicate nonlocal counterpart of the unique…
We consider a class of singular perturbations to the stochastic heat equation or semilinear variations thereof. The interesting feature of these perturbations is that, as the small parameter epsilon tends to zero, their solutions converge…
This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…
We study the theory of equations in one variable over polyhedral semirings. The article revolves around a notion of solution to a polynomial equation over a polyhedral semiring. Our main results are a characterisation of local solutions in…