We solve the Calderón inverse conductivity problem [Calderón (1980, 2006)], for an elliptic type equation in a rectangular plane domain, to recover an unknown conductivity function inside the domain, from the over-specified Cauchy data on the bottom of the rectangle. The Calderón inverse problem exhibits threefold simultaneous difficulties: ill-posedness of the inverse Cauchy problem, illposedn...

Received: January 10, 2011 Accepted: February 10, 2011 doi:10.5539/jmr.v3n3p32 Abstract In this paper we obtained the formula for the common solution of the linear differential equation of the second order with the variable coefficients in the more common case. We also obtained the formula for the solution of the Cauchy problem.

Abstract. Here we utilize operator–valued Lq → Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integrodifferential equations in R. Moreover, we investigate separability properties of parabolic convolution operator equations that arise in heat conduction problems in materials with fading memory. Finally, we give some remarks on optimal regularity of ...

We prove convergence of the Adomian decomposition method for an abstract initial-value problem using the method of majorants from the Cauchy-Kowalevskaya theorem for differential equations with analytic vector fields. Convergence rates of the Adomian method are investigated in the context of the nonlinear Schrödinger equation. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq...