Series solutions of time-fractional PDEs by homotopy analysis method.
Singular solutions of the Briot-Bouquet type partial differential equations
Solutions Globales Régulières pour Quelques Équations Lineaires D'évolution du Type Pseudo-Différentiel Singulier
2000 Mathematics Subject Classification: 35C15, 35D05, 35D10, 35S10, 35S99.We give here examples of equations of type (1) ∂tt2 y -p(t, Dx) y = 0, where p is a singular pseudo-differential operator with regular global solutions when the Cauchy data are regular, t ∈ R, x ∈ R5.
Solutions in Gevrey spaces of partial differential equations with constant coefficients
Si dà una condizione sufficiente per la esistenza di una soluzione in uno spazio di Gevrey , razionale , , di una equazione lineare a derivate parziali a coefficienti costanti , quando . La dimostrazione completa dei risultati ottenuti è contenuta in una nota dell’autore in corso di pubblicazione su "Astérisque".
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).
Solutions to a class of polynomially generalized Bers–Vekua equations using Clifford analysis
In this paper a class of polynomially generalized Vekua–type equations and of polynomially generalized Bers–Vekua equations with variable coefficients defined in a domain of Euclidean space are discussed. Using the methods of Clifford analysis, first the Fischer–type decomposition theorems for null solutions to these equations are obtained. Then we give, under some conditions, the solutions to the polynomially generalized Bers–Vekua equation with variable coefficients. Finally, we present the structure...
Solutions to some nonlinear PDE's in the form of Laplace type integrals
A nonlinear equation in 2 variables is considered. A formal solution as a series of Laplace integrals is constructed. It is shown that assuming some properties of Char P, one gets the Gevrey class of such solutions. In some cases convergence “at infinity” is proved.
Solving initial-boundary value problems for coupled systems of partial differential equations
Some Linear Elliptic Selfsimilar Equations with Whirl-Like Solutions.
Spectral Analysis of the Laplacian in Domains with Cylinders.
Summability of power series in several variables, with applications to singular perturbation problems and partial differential equations
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