共查询到20条相似文献,搜索用时 15 毫秒
1.
M. A. Raupp R. A. Feijóo C. A. de Moura 《Bulletin of the Brazilian Mathematical Society》1978,9(2):39-61
In this paper we present the analysis of an algorithm of Uzawa type to compute solutions of the quasi variational inequality $$\begin{gathered} (QVI)\left( {\frac{{\partial ^2 u}}{{\partial t^2 }},\upsilon - \frac{{\partial u}}{{\partial t}}} \right) + \left( {\frac{{\partial u}}{{\partial x}},\frac{{\partial \upsilon }}{{\partial x}} - \frac{{\partial ^2 u}}{{\partial x\partial t}}} \right) + \left( {\frac{{\partial ^2 u}}{{\partial x\partial t}},\frac{{\partial \upsilon }}{{\partial x}} - \frac{{\partial ^2 u}}{{\partial x\partial t}}} \right) + \hfill \\ + \left[ {u(1,t) + \frac{{\partial u}}{{\partial t}}(1,t)} \right]\left[ {\upsilon (1) - \frac{{\partial u}}{{\partial t}}(1,t)} \right] + J(u;\upsilon ) - J\left( {u;\frac{{\partial u}}{{\partial t}}} \right) \geqslant \hfill \\ \geqslant \left( {f,\upsilon - \frac{{\partial u}}{{\partial t}}} \right) + F(t)\left[ {\upsilon (0) - \frac{{\partial u}}{{\partial t}}(0,t)} \right],t > 0,\forall \upsilon \in H^1 (0,1), \hfill \\ \end{gathered} $$ which is a model for the dynamics of a pile driven into the ground under the action of a pile hammer. In (QVI) (...) is the scalar product inL 2(0, 1) andJ(u;.) is a convex functional onH 1(0, 1), for eachu, describing the soil-pile friction effect. 相似文献
2.
Asymptotic behavior of the solution of a nonlinear integro-differential diffusion equation 总被引:1,自引:0,他引:1
We study the asymptotic behavior as t → ∞ of the solution of the initial-boundary value problem for the nonlinear integro-differential equation where a(S) = (1 + S) p , 0 < p ≤ 1. We consider problems with homogeneous boundary conditions as well as with a nonhomogeneous boundary condition on part of the boundary. The orders of convergence are established.
相似文献
$$\frac{{\partial U}}{{\partial t}} = \frac{\partial }{{\partial x}}\left[ {a\left( {\mathop \smallint \limits_0^t \left( {\frac{{\partial U}}{{\partial x}}} \right)^2 d\tau } \right)\frac{{\partial U}}{{\partial x}}} \right],$$
3.
I. V. Denisov 《Computational Mathematics and Mathematical Physics》2018,58(4):562-571
A singularly perturbed parabolic equation is considered in a rectangle with boundary conditions of the first kind. The function F at the corner points of the rectangle is assumed to be monotonic with respect to the variable u on the interval from the root of the degenerate equation to the boundary condition. A complete asymptotic expansion of the solution as ε → 0 is constructed, and its uniformity in the closed rectangle is proven.
相似文献
$${\varepsilon ^2}\left( {{{\text{a}}^2}\frac{{{\partial ^2}u}}{{\partial {x^2}}} - \frac{{\partial u}}{{\partial t}}} \right) = F\left( {u,x,t,\varepsilon } \right)$$
4.
A. H. Babayan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2007,42(4):177-183
A boundary value problem for the Bitsadze equation in the interior of the unit disc is considered. It is proved that the problem is Noetherian and its index is calculated, and solvability conditions for the non-homogeneous problem are proposed. Some solutions of the homogeneous problem are explicitely found.
相似文献
$\frac{{\partial ^2 }}{{\partial \bar z^2 }}u(x,y) \equiv \frac{1}{4}\left( {\frac{\partial }{{\partial x}} + i\frac{\partial }{{\partial y}}} \right)^2 u(x,y) = 0$
5.
D. T. Luyen 《Mathematical Notes》2017,101(5-6):815-823
In this paper, we study the existence of multiple solutions for the boundary-value problem where Ω is a bounded domain with smooth boundary in R N (N ≥ 2) and Δ γ is the subelliptic operator of the type We use the three critical point theorem.
相似文献
$${\Delta _\gamma }u + f\left( {x,u} \right) = 0in\Omega ,u = 0on\partial \Omega ,$$
$${\Delta _\gamma }u = \sum\limits_{j = 1}^N {{\partial _{{x_j}}}\left( {\gamma _j^2{\partial _{{x_j}}}u} \right)} ,{\partial _{{x_j}}}u = \frac{{\partial u}}{{\partial {x_j}}},\gamma = \left( {{\gamma _1},{\gamma _2}, \ldots ,{\gamma _N}} \right).$$
6.
We study the break-down mechanism of smooth solution for the gravity water-wave equation of infinite depth. It is proved that if the mean curvature κ of the free surface Σt, the trace(V, B) of the velocity at the free surface, and the outer normal derivative ?P/?n of the pressure P satisfy sup t∈[0,T]||κ(t)||~(Lp∩L~2+∫~T_0||(▽V, ▽B)(t)||~6_(L∞)dt+∞,inf (t,x,y)∈[0,T]×Σ_t-?P/?n(t, x, y)≥c0,for some p 2d and c_0 0, then the solution can be extended after t = T. 相似文献
7.
Another method for computing the densities of integrals of motion for the Korteweg-de Vries equation
B. M. Levitan 《Mathematical Notes》1977,22(1):562-565
In the first section of this article a new method for computing the densities of integrals of motion for the KdV equation is given. In the second section the variation with respect to q of the functional ∫ 0 π w (x,t,x,;q)dx (t is fixed) is computed, where W(x, t, s; q) is the Riemann function of the problem $$\begin{gathered} \frac{{\partial ^z u}}{{\partial x^2 }} - q(x)u = \frac{{\partial ^2 u}}{{\partial t^2 }} ( - \infty< x< \infty ), \hfill \\ u|_{t = 0} = f(x), \left. {\frac{{\partial u}}{{\partial t}}} \right|_{t = 0} = 0. \hfill \\ \end{gathered} $$ 相似文献
8.
We investigate the initial-boundary value problem for the nonlinear equation system $$\frac{{\partial u}}{{\partial t}} = A\frac{{\partial ^2 u}}{{\partial x^2 }} + f(u) + g(u)\frac{{\partial u}}{{\partial x}},$$ whereA is a complex diagonal matrix,f andg are complex vector-functions. The convergence and stability in theW 2 2 norm of the proposed Crank-Nicolson type difference schemes is proved. No restrictions on the ratio of time and space grid steps are assumed. 相似文献
9.
A. V. Martynenko A. F. Tedeev 《Computational Mathematics and Mathematical Physics》2008,48(7):1145-1160
The Cauchy problem for a degenerate parabolic equation with a source and inhomogeneous density of the form is studied. Time global existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of the solution are obtained in the case of global solvability.
相似文献
$\rho (x)\frac{{\partial u}}{{\partial t}} = div(u^{m - 1} \left| {Du} \right|^{\lambda - 1} Du) + \rho (x)u^p $
10.
M. RadziŪnas 《Lithuanian Mathematical Journal》1996,36(2):178-194
The first and the second boundary value problems for a system of nonlinear equations of Schrödinger type $$\frac{{\partial u}}{{\partial t}} = A\frac{{\partial u}}{{\partial x}} + iB\frac{{\partial ^2 u}}{{\partial x^2 }} + f\left( {u, u*} \right)$$ are investigated. HereA andB are real and real positive definite, respectively, constant diagonal matrices, f is a polynomial complex vector function. We do not try to get rid of the addend A?u/?x. Using a new type ofa priori estimates, convergence and stability of difference schemes of Crank-Nicolson type for these problems in W 2 1 norm are proved. No restrictions on the ratio of time and space grid steps are assumed. 相似文献
11.
A. Martin 《Journal of Theoretical Probability》2004,17(3):693-703
We examine the small ball asymptotics for the weak solution X of the stochastic wave equation
on the real line with deterministic initial conditions. 相似文献
12.
We derive sharp L∞(L 1 ) a posteriori error estimate for the convection dominated diffusion equations of the form The derived estimate is insensitive to the diffusion parameter ε → 0. The problem is discretized implicitly in time via the method of characteristics and in space via continuous piecewise linear finite elements. Numerical experiments are reported to show the competitive behavior of the proposed adaptive method.
相似文献
$$\frac{{\partial u}}{{\partial t}} + div(vu) - \varepsilon \Delta u = g.$$
13.
Christer Borell 《Probability Theory and Related Fields》1991,87(3):403-409
Suppose a, b, and are reals witha<b and consider the following diffusion equation
相似文献
14.
A. P. Oskolkov 《Journal of Mathematical Sciences》1978,10(1):95-103
For the system of Navier-Stokes-Voigt equations $$\frac{{\partial \vec v}}{{\partial t}} - v\Delta \vec v - \aleph \frac{{\partial \Delta \vec v}}{{\partial t}} + v_\kappa \frac{{\partial \Delta \vec v}}{{\partial x_\kappa }} + grad \rho = 0, div \vec v = 0$$ and the BBM equation $$\frac{{\partial v}}{{\partial t}} + v\frac{{\partial \Delta v}}{{\partial x}} - \frac{{\partial ^3 v}}{{\partial t\partial x^2 }} = 0$$ characteristic functions \(\mathcal{F}\left( {\vec \theta ;t} \right)\) of the measure μt(ω)=μ(V ?1 t (ω)), describing the evolution in time of the probability measure μ(ω) defined on the set of initial conditions for the first initial boundary-value problem for system (1) or Eq. (2) are constructed and investigated. It is shown that the characteristic functions \(\mathcal{F}\left( {\vec \theta ;t} \right)\) constructed satisfy partial differential equations with an infinite number of independent variables (t; θ1,θ2,...) [the statistical equations of E. Hopf for the system (1) or Eq. (2)]. 相似文献
15.
A. V. Martynenko A. F. Tedeev 《Computational Mathematics and Mathematical Physics》2007,47(2):238-248
The following quasilinear parabolic equation with a source term and an inhomogeneous density is considered: 相似文献
$\rho (x)\frac{{\partial u}}{{\partial t}} = div(u^{m - 1} \left| {Du} \right|^{\lambda - 1} Du) + u^p $ 16.
Sirkka -Liisa Eriksson-Bique Kirsti Oja-Kontio 《Advances in Applied Clifford Algebras》2001,11(2):181-189
We considerC
2-solutionsf=u+iv+jw of the system
17.
L. P. Kuptsov 《Mathematical Notes》1974,15(3):280-286
For an equation of the form $$\begin{gathered} \frac{{\partial u}}{{\partial t}} - \sum\nolimits_{ij = 1}^n {{\text{ }}\alpha ^{ij} } \frac{{\partial ^2 u}}{{\partial x^i \partial x^j }} + \sum\nolimits_{ij = 1}^n {\beta _j^i x^i } \frac{{\partial u}}{{\partial x^i }} = 0, \hfill \\ {\text{ }}x \in R^n ,{\text{ }}t \in R^1 , \hfill \\ \end{gathered}$$ where α=(αij) is a constant nonnegative matrix andΒ=(Β i i ) is a constant matrix, subject to certain conditions, we construct a fundamental solution, similar in its structure to the fundamental solution of the heat conduction equation; we prove a mean value theorem and show that u(x0, t0) can be represented in the form of the mean value of u(x, t) with a nonnegative density over a level surface of the fundamental solution of the adjoint equation passing through the point (x0, t0); finally, we prove a parabolic maximum principle. 相似文献
18.
A simple qualitative model of dynamic combustion
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