共查询到10条相似文献,搜索用时 109 毫秒
1.
V. L. Kamynin 《Differential Equations》2012,48(2):214-223
We study the existence and uniqueness of the solution of the inverse problem of finding an unknown coefficient b(x) multiplying the lower derivative in the nondivergence parabolic equation on the plane. The integral of the solution with
respect to time with some given weight function is given as additional information. The coefficients of the equation depend
on the time variable as well as the space variable. 相似文献
2.
Jason J. Sharples 《Journal of Differential Equations》2004,202(1):111-142
We consider linear parabolic equations of second order in a Sobolev space setting. We obtain existence and uniqueness results for such equations on a closed two-dimensional manifold, with minimal assumptions about the regularity of the coefficients of the elliptic operator. In particular, we derive a priori estimates relating the Sobolev regularity of the coefficients of the elliptic operator to that of the solution. The results obtained are used in conjunction with an iteration argument to yield existence results for quasilinear parabolic equations. 相似文献
3.
A parabolic variational inequality is investigated which comes from the study of the optimal exercise strategy for the perpetual American executive stock options in financial markets. It is a degenerate parabolic variational inequality and its obstacle condition depends on the derivative of the solution with respect to the time variable. The method of discrete time approximation is used and the existence and regularity of the solution are established. 相似文献
4.
The regularity of the Cauchy problem for a generalized Camassa-Holm type equation is investigated. The pseudoparabolic regularization approach is employed to obtain some prior estimates under certain assumptions on the initial value of the equation. The local existence of its solution in Sobolev space Hs (R) with 1 〈 s ≤ 3/2 is derived. 相似文献
5.
I. G. Mamedov 《Differential Equations》2014,50(3):415-418
For a fourth-order pseudoparabolic equation with nonsmooth coefficients in a rectangular domain, we consider the Dirichlet problem with nonclassical conditions that do not require matching conditions. We justify the equivalence of these conditions and the classical boundary conditions for the case in which the solution of the problem is sought in a Sobolev space. 相似文献
6.
《Journal de Mathématiques Pures et Appliquées》2006,85(3):371-414
This paper is devoted to continuity results of the time derivative of the solution to the one-dimensional parabolic obstacle problem with variable coefficients. Under regularity assumptions on the obstacle and on the coefficients, we prove that the time derivative of the solution is continuous for almost every time. When the solution is nondecreasing in time this result holds for every time. We also give an energy criterion which characterizes the continuity of the time derivative of the solution at a point of the free boundary. Such a problem arises in the pricing of American options in generalized Black–Scholes models of finance. Our results apply in financial mathematics. 相似文献
7.
We consider the inverse problem for a one-dimensional parabolic equation with unknown time-depending coefficients of the derivatives with respect to the space variable. We establish a condition for existence of a solution on some time interval whose length depends on the initial data of the problem. Uniqueness of a solution holds on the whole time interval. 相似文献
8.
Lingling Hou & Pengcheng Niu 《偏微分方程(英文版)》2020,33(4):341-376
In this paper we consider the divergence parabolic equation with bounded and measurable coefficients related to Hörmander's vector fields and establish a Nash type result, i.e., the local Hölder regularity for weak solutions. After deriving the parabolic Sobolev inequality, (1,1) type Poincaré inequality of Hörmander's vector fields and a De Giorgi type Lemma, the Hölder regularity of weak solutions to the equation is proved based on the estimates of oscillations of solutions and the isomorphism between parabolic Campanato space and parabolic Hölder space. As a consequence, we give the Harnack inequality of weak solutions by showing an extension property of positivity for functions in the De Giorgi class. 相似文献
9.
M. Kh. Beshtokov 《Russian Mathematics (Iz VUZ)》2018,62(10):1-14
In this paper we consider a boundary-value problems for degenerating pseudoparabolic equation with variable coefficients and with Gerasimov–Caputo fractional derivative. To solve the problem we obtain a priori estimates in differential and difference settings. These a priori estimates imply uniqueness and stability of the solution with respect to the initial data and the right-hand side on the layer, as well as the convergence of the solution of each of the difference problem to the solution of the corresponding differential problem. 相似文献
10.
We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an L p function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions. 相似文献