Lie symmetry method is applied to find analytic solutions of initial-boundaryvalue problems of transient conduction in semi-infinite solid with constant surface temperature or constant heat flux condition. The solutions are obtained in a manner highlighting the systematic procedure of extending the symmetry method for a PDE to investigate BVPs of the PDE. A comparative analysis of numerical and...

The modal formalism is developed to deal with index-modulated structures ended by anisotropic regions (perfectly matched layers, PML). The method is applicable to scattering problems from dielectric or metallic objects as well as to propagation in planar slab waveguides. The boundaryvalue problem is solved and the dispersion relation inside the PML is derived. The general expression of the eige...

The problem that is studied concerns a yawed wedge under a free surface, moving at a uniform speed. The model involves a trailing cavity whose boundary is a dividing streamline through the vertex of the wedge. The cavity closure mechanism is described according to the Tulin– Terent’ev single-spiral-vortex model. A closed-form solution to the governing nonlinear boundaryvalue problem is found by...

Abstract. We develop a calculus for nonlocal operators that mimics Gauss’ theorem and the Green’s identities of the classical vector calculus. The operators we define do not involve the derivatives. We then apply the nonlocal calculus to define variational formulations of nonlocal “boundaryvalue” problems that mimic the Dirichlet and Neumann problems for second-order scalar elliptic partial dif...

In this paper we analyze the global existence of classical solutions to the initial boundaryvalue problem for a nonlinear parabolic equation describing the collective behavior of an ensemble of neurons. These equations were obtained as a diffusive approximation of the mean-field limit of a stochastic differential equation system. The resulting Fokker-Planck equation presents a nonlinearity in t...

In general the mathematical model for steady, one-dimensional conduction in fins appears as a nonlinear, two-point boundaryvalue problem. The nonlinearities arise due to radiative surface heat transfer, temperature dependent thermal conductivity or heat transfer coefficient etc. [i]. Often in such cases a numerical solution has to be obtained. Examining the literature reporting such solutions i...

Macro-elements of arbitrary smoothness are constructed on Powell-Sabin triangle splits. These elements are useful for solving boundaryvalue problems and for interpolation of Hermite data. It is shown that they are optimal with respect to spline degree, and we believe they are also optimal with respect to the number of degrees of freedom. The construction provides local bases for certain supersp...

In this paper, we consider the characteristic initial–boundary value problem (IBVP) for the multi-dimensional Jin–Xin relaxation model in a half-space with arbitrary space dimension n52: As in the one-dimensional case (n 1⁄4 1; see (J. Differential Equations, 167 (2000), 388–437), our main interest is on the precise structural stability conditions on the relaxation system, particularly the form...

in this paper, we investigate the goursat problem in the class c21(d)cn0 (d  p) c00 (d q)for a third order pseudoparabolic equation. some results are given concerning the existence and uniquenessfor the solution of the suggested problem.