A mixed boundary value problem for the Laplace equation in an angle (1st part)
A new technique in constructing closed-form solutions for nonlinear PDEs appearing in fluid mechanics and gas dynamics.
A note on surfaces with radially symmetric nonpositive Gaussian curvature
It is easily seen that the graphs of harmonic conjugate functions (the real and imaginary parts of a holomorphic function) have the same nonpositive Gaussian curvature. The converse to this statement is not as simple. Given two graphs with the same nonpositive Gaussian curvature, when can we conclude that the functions generating their graphs are harmonic? In this paper, we show that given a graph with radially symmetric nonpositive Gaussian curvature in a certain form, there are (up to) four families...
A note to the Fourier method of solving partial second-order differential equations
A note to the Laplace transformation
An approximate analytic solution of a particular boundary value problem.
An explicit separate solution for the Tzitzeica equation.
An explicit solution to a system of implicit differential equations
Analysis of boundary bubbling solutions for an anisotropic Emden–Fowler equation
Analytical solution of a general boundary value problem for a BKW-equation.
Analytical solution of the hyperbolic heat conduction equation for moving semi-infinite medium under the effect of time-dependent laser heat source.
Applications of the Poincaré inequality to extended Kantorovich method.
Asymptotic solution of the Signorini problem of a beam lying on rigid bases.
Asymptotically self-similar solutions for the parabolic system modelling chemotaxis
We consider a nonlinear parabolic system modelling chemotaxis , in ℝ², t > 0. We first prove the existence of time-global solutions, including self-similar solutions, for small initial data, and then show the asymptotically self-similar behavior for a class of general solutions.
Auto-Bäcklund transformation and exact analytical solutions for the Kupershmidt equation.
Bäcklund transformations for several cases of a type of generalized KdV equation.
Beitrag zur Theorie der linearen partiellen Differentialgleichungen.
Bergmannsche Polynom-Erzeugende erster Art.
Boundary value problems of generalized axially symmetric Helmholtz equations
Computing exact solutions to a generalized Lax-Sawada-Kotera-Itô seventh-order KdV equation.