A boundary value problem for cold plasma dynamics.
A boundary value problem for mixed-type equations in domains with multiply connected hyperbolicity subdomains.
A finite element method for the nonlinera Tricomi problem.
A general investigation of admissible couplings between systems of higher order and different type
A generalization of the Hille--Yosida theorem to the case of degenerate semigroups in locally convex spaces.
A problem with internal conditions for a pseudoparabolic equation.
A simple bioclogging model that accounts for spatial spreading of bacteria.
About one high-order linear equation of mixed type.
About the decay of surface waves on viscous fluids without surface tension
We study the decay of the motions of a viscous fluid subject to gravity without surface tension with a free boundary at the top. We show that the solutions of the linearization about the equilibrium state decay, but not exponentially in a uniform manner. We also discuss the consequences of this for the non-linear equations.
An Analog of the Tricomi Problem for a Mixed Type Equation with a Partial Fractional Derivative
Mathematics Subject Classification 2010: 35M10, 35R11, 26A33, 33C05, 33E12, 33C20.The paper deals with an analog of Tricomi boundary value problem for a partial differential equation of mixed type involving a diffusion equation with the Riemann-Liouville partial fractional derivative and a hyperbolic equation with two degenerate lines. By using the properties of the Gauss hypergeometric function and of the generalized fractional integrals and derivatives with such a function in the kernel, the uniqueness...
Application of complex analysis to second order equations of mixed type
This paper deals with an application of complex analysis to second order equations of mixed type. We mainly discuss the discontinuous Poincaré boundary value problem for a second order linear equation of mixed (elliptic-hyperbolic) type, i.e. the generalized Lavrent’ev-Bitsadze equation with weak conditions, using the methods of complex analysis. We first give a representation of solutions for the above boundary value problem, and then give solvability conditions via the Fredholm theorem for integral...
Asymptotic behaviour of a class of degenerate elliptic-parabolic operators: a unitary approach
We study the asymptotic behaviour of a sequence of strongly degenerate parabolic equations with , . The main problem is the lack of compactness, by-passed via a regularity result. As particular cases, we obtain G-convergence for elliptic operators , G-convergence for parabolic operators , singular perturbations of an elliptic operator and , possibly .
Asymptotic representations for solutions of bisingular problems.