Related papers: Introduction to Mathematical Physics. Calculus of …
In this paper we study nonlinear second-order differential inclusions involving the ordinary vector $p$-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions. Our framework is general and unifying…
This course is intended as an introduction to the analysis of elliptic partial differential equations. The objective is to provide a large overview of the different aspects of elliptic partial differential equations and their modern…
Nonlinear boundary value problems (BVPs) by means of the classical Lie symmetry method are studied. A new definition of Lie invariance for BVPs is proposed by the generalization of existing those on much wider class of BVPs. A class of…
Solutions of the Dirichlet and Robin boundary value problems for the multi-term variable-distributed order diffusion equation are studied. A priori estimates for the corresponding differential and difference problems are obtained by using…
Basic principles of mathematical modeling are reviewed in this book, with the focus on physics and its practical applications, and examples of selected mathematical methods are presented. Most of the models have been imported from physics…
Boundary value problems for linear stationary dispersive equations of order $2l+1$, $l\in \mathbb{N}$ have been considered on finite intervals $(0,L)$. The existence and uniqueness of regular solutions have been established for general…
Finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
The method of separation of variables is significant, it has been applied to physics, engineering , chemistry and other fields. It allows to reduce the diffculity of problems by separating the variables from partial differential equation…
We introduce a fractional theory of the calculus of variations for multiple integrals. Our approach uses the recent notions of Riemann-Liouville fractional derivatives and integrals in the sense of Jumarie. Main results provide fractional…
In this paper, some initial-boundary-value problems for the time-fractional diffusion equation are first considered in open bounded n-dimensional domains. In particular, the maximum principle well-known for the PDEs of elliptic and…
We introduce a stochastic fractional calculus. As an application, we present a stochastic fractional calculus of variations, which generalizes the fractional calculus of variations to stochastic processes. A stochastic fractional…
We study existence and uniqueness of solutions for second order ordinary stochastic differential equations with Dirichlet boundary conditions on a given interval. In the first part of the paper we provide sufficient conditions to ensure…
In this article, the authors survey and review the studies of boundary value problems for regular functions in Clifford analysis, which include theoretical foundations and useful methods. Its theoretical bases consist of the generalized…
A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all…
Many evolution problems in physics are described by partial differential equations on an infinite domain; therefore, one is interested in the solutions to such problems for a given initial dataset. A prominent example is the binary black…
Discrete approximations to the equation \begin{equation*} L_{cont}u = u^{(4)} + D(x) u^{(3)} + A(x) u^{(2)} + (A'(x)+H(x)) u^{(1)} + B(x) u = f, \; x\in[0,1] \end{equation*} are considered. This is an extension of the Sturm-Liouville case…
It is known that the unified transform method may be used to solve any well-posed initial-boundary value problem for a linear constant-coefficient evolution equation on the finite interval or the half-line. In contrast, classical methods…
This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter one finds in the second chapter the construction…
We define and study the properties of Darboux-type transformations between Sturm--Liouville problems with boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter (including the Dirichlet boundary…