Originally formulated in the context of topology optimization, the concept of topological derivative has also proved effective as a qualitative inversion tool for a wave-based identification of finite-sized objects. This approach remains, however, largely based on a heuristic interpretation of the topological derivative, whereas most other qualitative approaches to inverse scattering are backed...

In this Research Method of Line is used to find the approximation solution one dimensional singularly perturbed Burger equation given with initial and boundary conditions. First, domain discretized derivative involving spatial variable x replaced into functional values at each grid points by using central finite difference method. Then, resulting first-order linear ordinary differential solved ...

Abstract We discuss Meyers-Serrin’s type results for smooth approximations of functions $$b=b(t,x): \mathbb {R}\times {R}^n\rightarrow {R}^m$$ b = ( t , x ) : R <m...

where u : (0, T ]× Ω→ R is the unknown function, Ω ⊂ R is a bounded domain with a Lipschitz continuous boundary Γ, 0 < T <∞ and ∂νβ(u) denotes outside normal derivative. Function β : R → R is nondecreasing Lipschitz continuous function satisfying (2.1). Function f : (0, T ]×Ω×R→ R is Lipschitz continuous with Lipschitz constant Lf and satisfies (2.2). We denote g(t, x, s) : = γs+φ(t, x), where ...