Solvability of boundary value problems for operator-differential equations of mixed type: the degenerate case.
Solvable nonlinear evolution PDEs in multidimensional space.
Solving the Degenerate Complex Monge-Ampère Equation with One Concentrated Singularity.
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
Some common asymptotic properties of semilinear parabolic, hyperbolic and elliptic equations
We consider three types of semilinear second order PDEs on a cylindrical domain , where is a bounded domain in , . Among these, two are evolution problems of parabolic and hyperbolic types, in which the unbounded direction of is reserved for time , the third type is an elliptic equation with a singled out unbounded variable . We discuss the asymptotic behavior, as , of solutions which are defined and bounded on .
Some Examples For Nonlinear Superposition
Some examples for nonlinear superposition.
Some fast finite-difference solvers for two-dimensional evolutionary equations on special domains
The author proves the existence of the asymptotic error expansion to the Peaceman-Rachford finite-difference scheme for the first boundary value problem of the two-dimensional evolationary equation on the so-called uniform and nearly uniform domains. This expansion leads, by Richardson extrapolation, to a simple process for accelerating the convergence of the method. A numerical example is given.
Some generic properties of nonlinear second order diffusional type problem
We are interested of the Newton type mixed problem for the general second order semilinear evolution equation. Applying Nikolskij’s decomposition theorem and general Fredholm operator theory results, the present paper yields sufficient conditions for generic properties, surjectivity and bifurcation sets of the given problem.
Some nonexistence results for higher-order evolution inequalities in cone-like domains.
Some remarks on biharmonic elliptic problems with positive, increasing and convex nonlinearities.
Some remarks on time-dependent evolution systems in the hyperbolic case
Some solutions for a class of singular equations
In this paper we obtain all solutions which depend only on for a class of partial differential equations of higher order with singular coefficients.
Some theorems concerning partial differential equations
Some Uniqueness and Growth Theorems in the Cauchy Problem for P utt + M ut + Nu = 0 in Hilbert Space.
Spectral analysis of long wavelength periodic waves and applications.
Stabilité et convergence des méthodes spectrales polynômiales. Application à l'équation d'advection
Stability analysis of phase boundary motion by surface diffusion with triple junction
The linearized stability of stationary solutions for the surface diffusion flow with a triple junction is studied. We derive the second variation of the energy functional under the constraint that the enclosed areas are preserved and show a linearized stability criterion with the help of the -gradient flow structure of the evolution problem and the analysis of eigenvalues of a corresponding differential operator.
Stability and error estimates valid for infinite time, for strongly monotone and infinitely stiff evolution equations
Stability and saddle-point property for a linear autonomous functional parabolic equation