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-convergence techniques and relaxation results of constrained energy functionals are used to identify the limiting energy as the thickness approaches zero of a ferromagnetic thin structure , , whose energy is given bysubject toand to the constraintwhere is any continuous function satisfying -growth assumptions with . Partial results are also obtained in the case , under an additional assumption on .
Γ-convergence techniques and relaxation results of
constrained energy functionals are used to identify the limiting energy as the
thickness ε approaches zero of a ferromagnetic thin
structure , , whose
energy is given by
subject to
and to the constraint
where W is any continuous function satisfying p-growth assumptions
with p> 1.
Partial results are also obtained in the case p=1, under
an additional assumption on W.
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.
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...
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...
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 .
In the present paper we study the unique solvability of two non-local boundary value problems with continuous and special gluing conditions for parabolic-hyperbolic type equations. The uniqueness of the solutions of the considered problems are proven by the “abc” method. Existence theorems for the solutions of these problems are proven by the method of integral equations. The obtained results can be used for studying local and non-local boundary-value problems for mixed-hyperbolic type equations...
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