Results 141 to 150 of about 5,520,045 (177)

On the Goursat classification problem

Programming and Computer Software, 2012
In the paper, the Goursat problem--classification of nonlinear hyperbolic differential equations possessing two characteristic invariants--is considered. An algorithm for finding the characteristic invariants is described. On the basis of the algorithm implemented in REDUCE, the characteristic invariants of two Laine's equations are verified.
O V Kaptsov
exaly   +2 more sources

A nonlinear goursat problem with irregular data

Integral Transforms and Special Functions, 1998
With the help of differential algebras of(C,Ep)-type, we construct an algebra of generalized functions which allows us to solve a Gourmet problem with irregular data. For this problem, we perform a qualitative study when the data are Dirac functions.
Nuiro, Silvere, Marti, Jean-André, Valmorin, Vincent   +2 more
exaly   +3 more sources

Goursat-Type Problem for a Higher-Order Equation [PDF]

Ukrainian Mathematical Journal, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Юсубов, Ш.Ш.
core   +5 more sources

Multidimensional goursat problem for semilinear hyperbolic equations

Applied Mathematics, 1996
We are concerned with the following fully semilinear Goursat problem \[ Pu= f(x, t, u, \nabla u),\quad (x, t)\in \Gamma,\quad u|_{\partial \Gamma}= 0, \] where \((x, t)\in \mathbb{R}^3\), \(P\equiv P(x, t, \partial_{x_1}, \partial_{x_2}, \partial_t)= \partial^2_t+ \sum^2_{|\alpha|= 1} a_\alpha(x, t) \partial^\alpha \partial^{2- |\alpha|}+ R_1\).
Daoyuan Fang
exaly   +2 more sources

On the Goursat problem for a linear partial differential equation [PDF]

, 2011
In this paper, the Goursat problem of a general form for a linear partial differential equation is investigated with the help of the Riemann function method. Some results are given concerning the existence and uniqueness for the solution of the suggested problem.
Maher A., Utkina Y.
openaire   +4 more sources

On existence and nonexistence of global solutions of Cauchy–Goursat problem for nonlinear wave equations [PDF]

Journal of Mathematical Analysis and Applications, 2008
We consider the Cauchy–Goursat initial characteristic problem for nonlinear wave equations with power nonlinearity. Depending on the power of nonlinearity and the parameter in an equation we investigate the problem on existence and nonexistence of global
Jokhadze, O., O. Jokhadze
exaly   +2 more sources

Goursat Problem for the Factorizable Hyperbolic Equation in Two Independent Variables

Mathematical and Computational Applications, 2003
For the scalar linear hyperbolic partial differential equations (PDEs) in two independent variables to be factorizable, the Laplace invariants h or k must be zero.
Fazal Mahomed
exaly   +2 more sources

On the numerical solution of the Goursat problem

BIT Numerical Mathematics, 1971
J T Day
exaly   +3 more sources

Strong scheme for a stochastic Goursat problem

Applied Mathematics and Computation, 2004
The authors construct a strong scheme for a stochastic Goursat problem and prove the mean-square convergence to its solution for the approximation generated by the strong scheme. Moreover, they obtain the rate of convergence for the strong scheme.
Shu-Shiang Huang, Yenkun Huang, Che-Yuan Tsai   +2 more
openaire   +3 more sources

Uniqueness and Goursat problems

Annali di Matematica Pura ed Applicata, 1969
A uniqueness theorem by W. Walter for a second order Goursat problem in to independent variables is generalized. In the resulting theorem there are no restrictions on the order or on the number of indipendent variables.
openaire   +1 more source