Uniqueness for boundary value problems for second order finite difference equations

We establish maximum principles for second order difference equations and apply them to obtain uniqueness for solutions of some boundary value problems.

A Computer Algebra Application to Determination of Lie Symmetries of Partial Differential Equations

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006

Solutions of Analytical Systems of Partial Differential Equations

In this paper are examined some classes of linear and non-linear analytical systems of partial differential equations. Compatibility conditions are found and if they are satisfied, the solutions are given as functional series in a neighborhood of a given point (x = 0).

Integral Inequalities and Applications to Partial Differential Equations with “Maxima”

Кремена В. Стефанова - В тази статия са разрешени някои нелинейни интегрални неравенства, които включват максимума на неизвестната функция на две променливи. Разгледаните неравенства представляват обобщения на класическото неравенство на Гронуол-Белман. Значението на тези интегрални неравенства се определя от широките им приложения в качествените изследвания на частните диференциални уравнения с “максимуми” и е илюстрирано чрез някои директни приложения.

Hypoellipticity of Anisotropic Partial Differential Equations

2002 Mathematics Subject Classification: 35S05

Gevrey Local Solvability for Semilinear Partial Differential Equations

2002 Mathematics Subject Classification: 35S05

Oscillation Criteria of Second-Order Quasi-Linear Neutral Delay Difference Equations

2000 Mathematics Subject Classification: 39A10.

Exterior Differential Systems and Euler-Lagrange Partial Differential Equations

The book also covers the Second Variation, Euler-Lagrange PDE systems, and higher-order conservation laws.

A posteriori error estimation for discontinuous Galerkin discretizations of H(curl)-elliptic partial differential equations

We develop the a posteriori error estimation of interior penalty discontinuous Galerkin discretizations for H(curl)-elliptic problems that arise in eddy current models. Computable upper and lower bounds on the error measured in terms of a natural (mesh-dependent) energy norm are derived. The proposed a posteriori error estimator is validated by numerical experiments, illustrating its reliability and efficiency for a range of test problems.

Classification of discrete systems on a square lattice

We consider the classification up to a Möbius transformation of real linearizable and integrable partial difference equations with dispersion defined on a square lattice by the multiscale reduction around their harmonic solution. We show that the A1, A2, and A3 linearizability and integrability conditions constrain the number of parameters in the equation, but these conditions are insufficient for a complete characterization of the subclass of multilinear equations on a square lattice.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

Existence of solutions for second order partial neutral functional differential equations

We establish existence of mild solutions for a class of abstract second-order partial neutral functional differential equations with unbounded delay in a Banach space.