Let $${\mathcal {L}}=\sum _{j=1}^{m}X_{j}^{2}$$ be a Hörmander sum of squares vector fields in $${\mathbb {R}}^{n}$$ , where any $$X_{j}$$ is homogeneous degree 1 with respect to family non-isotropic dilations . Then, {L}}$$ known admit global fundamental solution $$\Gamma (x;y)$$ that can represented as the integral sublaplacian operator on lifting space {R}}^{n}\times {\mathbb {R}}^{p}$$ equi...

We consider the linear field-road system, a model for fast diffusion channels in population dynamics and ecology. This system takes form of PDEs set on domains different dimensions, with exchange boundary conditions. Despite intricate geometry problem, we provide an explicit expression its fundamental solution to associated Cauchy problem. The main tool is Fourier (on road variable)/Laplace tim...

We study solutions of almost periodic linear differential systems. This field is called the Favard theory what is based on the famous Favard result in [10] (see, e.g., [3, Theorem 1.2] or [28, Theorem 1]). It is a well-known corollary of the Favard (and the Floquet) theory that any bounded solution of a periodic linear differential system is almost periodic (see [12, Corollary 6.5] and [13] for...

 Abstract: Determination of the diffusion coefficient on the base of solution of a linear inverse problem of the parameter estimation using the Least-square method is presented in this research. For this propose a set of temperature measurements at a single sensor location inside the heat conducting body was considered. The corresponding direct problem was then solved by the application of the ...