We prove null controllability for linear and semilinear heat equations with dynamic boundary conditions of surface diffusion type. The results are based on a new Carleman estimate for this type of boundary conditions.

‎in this paper‎, ‎we consider an inverse boundary value problem for two-dimensional heat equation in an annular domain‎. ‎this problem consists of determining the temperature on the interior boundary curve from the cauchy data (boundary temperature and heat flux) on the exterior boundary curve‎. ‎to this end‎, ‎the boundary integral equation method is used‎. ‎since the resulting system of linea...

When a (frequency–domain) boundary value problem involving a homogeneous linear material is solved to assess the validity of the Post constraint, a conflict arises between the fundamental differential equations of electromagnetism in the chosen material and a näive application of the usual boundary conditions. It is shown here that the conflict vanishes when the boundary conditions are properly...

An adaptive unstructured grid generation scheme is introduced to use finite volume (FV) and finite element (FE) formulation to solve the heat equation with singular boundary conditions. Regular grids could not acheive accurate solution to this problem. The grid generation scheme uses an optimal time complexity frontal method for the automatic generation and delaunay triangulation of the grid po...

The method of quasilinearization of Bellman and Kalaba [2] has been extended, refined, and generalized when the forcing function is the sum of a convex and concave function using coupled lower and upper solutions. This method is now known as the method of generalized quasilinearization. It has all the advantages of the quasilinearization method such that the iterates are solutions of linear sys...

It is known that, from a modeling point of view, fractional dynamic equations are more suitable compared to integer derivative models. In fact, equation referred as an with memory. To demonstrate that the model better than corresponding model, we need compute solutions differential and compare them relative data available. this work, will illustrate linear nq-order sequential Caputo equations, ...

Recently developed kinetic theory and related closures for neuronal network dynamics have been demonstrated to be a powerful theoretical framework for investigating coarse-grained dynamical properties of neuronal networks. The moment equations arising from the kinetic theory are a system of (1 + 1)-dimensional nonlinear partial differential equations (PDE) on a bounded domain with nonlinear bou...

In this paper, surface effects including surface elasticity, surface stress and surface density, on the free vibration analysis of Euler-Bernoulli and Timoshenko nanobeams are considered using nonlocal elasticity theory. To this end, the balance conditions between nanobeam bulk and its surfaces are considered to be satisfied assuming a linear variation for the component of the normal stress thr...

We propose dynamic non-linear equations for moving surfaces in an electromagnetic field. The field is induced by a material body with a boundary of the surface. Correspondingly the potential energy, set by the field at the boundary can be written as an addition of four-potential times four-current to a contraction of the electromagnetic tensor. Proper application of the minimal action principle...

In this paper we consider mesh approximations of a boundary value problem for singularly perturbed elliptic equations of convection-diffusion type on a strip. To approximate the equations, we use classical finite difference approximations on piecewise-uniform meshes condensing in a neighbourhood of the boundary layer. The approximation errors of solutions and derivatives are analysed in the ρ-m...