Related papers: Mean value methods for solving the heat equation b…
Mean field theory for the time evolution of quantum meson fields is studied in terms of the functional Schroedinger picture with a time-dependent Gaussian variational wave functional. We first show that the equations of motion for the…
In this paper, within scaling invariance theory, we define and apply to the numerical solution of a similarity boundary layer model an iterative transformation method. The boundary value problem to be solved depends on a parameter and is…
In this work, an accurate regularization technique based on the Meyer wavelet method is developed to solve the ill-posed backward heat conduction problem with time-dependent thermal diffusivity factor in an infinite "strip". In principle,…
We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…
In this paper, we introduce and study a new extragradient iterative process for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality for an…
In this paper we first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, we can obtain some strictly…
We consider a partial data inverse problem for a time-dependent convection-diffusion equation on an admissible manifold. We prove that the time-dependent convection term and time-dependent density can be recovered uniquely modulo a known…
We consider the problem of recovering the initial condition in the one-dimensional one-phase Stefan problem for the heat equation from the knowledge of the position of the melting point. We first recall some properties of the free boundary…
In this paper we employ the Renormalization Group (RG) method to study higher order corrections to the long-time asymptotics of a class of nonlinear integral equations with a generalized heat kernel and with time-dependent coefficients.…
We consider the mean-variance hedging problem under partial Information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is…
In this paper, we deal with the inverse source problem of determining a source in a time fractional diffusion equation where data are given at a fixed time. This problem is ill-posed, i.e., the solution does not depend continuously on the…
This paper studies proofs of strong convergence of various iterative algorithms for computing the unique zeros of set-valued accretive operators that also satisfy some weak form of uniform accretivity at zero. More precisely, we extract…
The (1+1)-dimensional nonlinear boundary value problem, modeling the process of melting and evaporation of metals, is studied by means of the classical Lie symmetry method. All possible Lie operators of the nonlinear heat equation, which…
Inverse optimization has received much attention in recent years, but little literature exists for solving generalized mixed integer inverse optimization. We propose a new approach for solving generalized mixed-integer inverse optimization…
Recent results concerning solutions of the modified Helmholtz equation are reviewed; namely, various mean value properties and their corollaries, converse and inverse of these properties, and relations between these solutions and harmonic…
In this paper a variant of nonlinear exponential Euler scheme is proposed for solving nonlinear heat conduction problems. The method is based on nonlinear iterations where at each iteration a linear initial-value problem has to be solved.…
It is well known that generic solutions of the heat equation are not analytic in time in general. Here it is proven that ancient solutions with exponential growth are analytic in time in ${\M} \times (-\infty, 0]$. Here $\M=\R^n$ or is a…
Integral equation based numerical methods are directly applicable to homogeneous elliptic PDEs, and offer the ability to solve these with high accuracy and speed on complex domains. In this paper, extensions to problems with inhomogeneous…
The study of the paper mainly focusses on recovering the dissipative parameter in a cascade system coupling a bilaplacian operator to a heat equation from final time measured data via quasi-solution based optimization. The coefficient…
Inverse initial and inverse source problems of a time-fractional differential equation with Bessel operator are considered. Results on existence and uniqueness of solutions to these problems are presented. The solution method is based on…