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Displaying 521 –
540 of
1688
We describe a constructive algorithm for obtaining smooth
solutions of a nonlinear, nonhyperbolic pair of balance laws
modeling incompressible two-phase flow in one space dimension and
time. Solutions are found as stationary solutions of a related
hyperbolic system, based on the introduction of an artificial time
variable.
As may be expected for such nonhyperbolic systems, in general the
solutions obtained do not satisfy both components of the given
initial data. This deficiency may be overcome,...
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).
MSC 2010: 35R11, 42A38, 26A33, 33E12The method of integral transforms based on joint application of a fractional generalization of the Fourier transform and the classical Laplace transform is utilized for solving Cauchy-type problems for the time-space fractional diffusion-wave equations expressed in terms of the Caputo time-fractional derivative and the Weyl space-fractional operator. The solutions obtained are in integral form whose kernels are Green functions expressed in terms of the Fox H-functions....
Some solutions are obtained for a class of singular semilinear elliptic equations with critical weighted Hardy-Sobolev exponents by variational methods and some analysis techniques.
Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac operator in Clifford analysis. This problem is a natural generalization of the Dirichlet problem.
Currently displaying 521 –
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1688