On the Cauchy problem of a quasilinear degenerate parabolic equation.
On the Cauchy-problem for generalized Kadomtsev-Petviashvili-II equations.
On the change of energy caused by crack propagation in 3-dimensional anisotropic solids
Crack propagation in anisotropic materials is a persistent problem. A general concept to predict crack growth is the energy principle: A crack can only grow, if energy is released. We study the change of potential energy caused by a propagating crack in a fully three-dimensional solid consisting of an anisotropic material. Based on methods of asymptotic analysis (method of matched asymptotic expansions) we give a formula for the decrease in potential energy if a smooth inner crack grows along a...
On the Chaplighin method for partial differential equations of the first order
On the Chaplyghin method for generalized solutions of partial differential functional equations.
On the Chaplygin method for partial differential-functional equations of the first order
On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations [Book]
On the characteristics for a system of partial differential equations of the first order in a special case
On the characterization of harmonic functions with initial data in Morrey space
Let be a metric measure space satisfying the doubling condition and an -Poincaré inequality. Consider the nonnegative operator generalized by a Dirichlet form on . We will show that a solution to on satisfies an -Carleson condition if and only if can be represented as the Poisson integral of the operator with the trace in the generalized Morrey space , where is a nonnegative function defined on a class of balls in . This result extends the analogous characterization founded...
On the Charney Conjecture of Data Assimilation Employing Temperature Measurements Alone: The Paradigm of 3D Planetary Geostrophic Model
Analyzing the validity and success of a data assimilation algorithmwhen some state variable observations are not available is an important problem in meteorology and engineering. We present an improved data assimilation algorithm for recovering the exact full reference solution (i.e. the velocity and temperature) of the 3D Planetary Geostrophic model, at an exponential rate in time, by employing coarse spatial mesh observations of the temperature alone. This provides, in the case of this paradigm,...
On the Chebyshev penalty method for parabolic and hyperbolic equations
On the choice of iteration parameters in the Stone incomplete factorization
The paper is concerned with the iterative solution of sparse linear algebraic systems by the Stone incomplete factorization. For the sake of clarity, the algorithm of the Stone incomplete factorization is described and, moreover, some properties of the method are derived in the paper. The conclusion is devoted to a series of numerical experiments focused on the choice of iteration parameters in the Stone method. The model problem considered showe that we can, in general, choose appropriate values...
On the circle criterion for boundary control systems in factor form : Lyapunov stability and Lur’e equations
A Lur’e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur’e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on results...
On the circle criterion for boundary control systems in factor form: Lyapunov stability and Lur'e equations
A Lur'e feedback control system consisting of a linear, infinite-dimensional system of boundary control in factor form and a nonlinear static sector type controller is considered. A criterion of absolute strong asymptotic stability of the null equilibrium is obtained using a quadratic form Lyapunov functional. The construction of such a functional is reduced to solving a Lur'e system of equations. A sufficient strict circle criterion of solvability of the latter is found, which is based on...
On the classification of the Lie algebras .
On the coincidence set in biharmonic variational inequalities with thin obstacles
On the collision of two solitons for the generalized KdV equation in the nonintegrable case
On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients
On the combined effect of boundary approximation and numerical integration on mixed finite element solution of 4th order elliptic problems with variable coefficients
Error estimates for the mixed finite element solution of 4th order elliptic problems with variable coefficients, which, in the particular case of aniso-/ortho-/isotropic plate bending problems, gives a direct, simultaneous approximation to bending moment tensor field and displacement field 'u', have been developed considering the combined effect of boundary approximation and numerical integration.
On the complete integrability of an equation having solitons but not known to have a lax pair.