共查询到20条相似文献,搜索用时 15 毫秒
1.
Nguyen Huy Tuan Dang Duc Trong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(6):1842-1852
Consider a nonlinear backward parabolic problem in the form
2.
Dang Duc Trong 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(9):4167-4176
We consider the inverse time problem for the nonlinear heat equation in the form
3.
Nguyen Huy Tuan Dang Duc Trong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(11):3479-3488
A nonlinear backward heat problem for an infinite strip is considered. The problem is ill-posed in the sense that the solution (if it exists) does not depend continuously on the data. In this paper, we use the Fourier regularization method to solve the problem. Some sharp estimates of the error between the exact solution and its regularization approximation are given. 相似文献
4.
Nguyen Huy Tuan Dang Duc Trong 《Nonlinear Analysis: Theory, Methods & Applications》2010,73(7):1966-1972
The nonlinear backward Cauchy problem
ut+Au(t)=f(u(t)),u(T)=φ, 相似文献
5.
In this article the authors consider a backward nonlinear heat equation. The uniqueness of the problem is proved and the problem is regularized by finite dimensional approximations. Error estimates in some particular cases are given. 相似文献
6.
Of concern is the uniformly parabolic problem
7.
We deal in detail with the question of existence, uniqueness and asymptotic behaviour of solutions to a parabolic equation with hysteresis and convection. This equation is part of a model system which describes the magnetohydrodynamic (MHD) flow of a conducting fluid between two ferromagnetic plates. The result of this paper complements the content of a previous paper of the first author, where existence of the solution has been proved under fairly general assumptions on the hysteresis operator and the uniqueness was only obtained for a restricted class of hysteresis operators. 相似文献
8.
In this paper, we study a kind of system of second order quasilinear parabolic partial differential equation combined with algebra equations. Introducing a family of coupled forward–backward stochastic differential equations, and by virtue of some delicate analysis techniques, we give a probabilistic interpretation for it in the viscosity sense. 相似文献
9.
In this paper we investigate the asymptotic behavior of the nonlinear Cahn–Hilliard equation with a logarithmic free energy and similar singular free energies. We prove an existence and uniqueness result with the help of monotone operator methods, which differs from the known proofs based on approximation by smooth potentials. Moreover, we apply the Lojasiewicz–Simon inequality to show that each solution converges to a steady state as time tends to infinity. 相似文献
10.
Markus Biegert 《Journal of Differential Equations》2009,247(7):1949-698
Let Ω⊂RN be a bounded domain and let μ be an admissible measure on ∂Ω. We show in the first part that if Ω has the H1-extension property, then a realization of the Laplace operator with generalized nonlinear Robin boundary conditions, formally given by on ∂Ω, generates a strongly continuous nonlinear submarkovian semigroup SB=(SB(t))t?0 on L2(Ω). We also obtain that this semigroup is ultracontractive in the sense that for every u,v∈Lp(Ω), p?2 and every t>0, one has
11.
In arbitrary dimension, in the discrete setting of finite-differences we prove a Carleman estimate for a semi-discrete parabolic operator, in which the large parameter is connected to the mesh size. This estimate is applied for the derivation of a (relaxed) observability estimate, that yield some controlability results for semi-linear semi-discrete parabolic equations. Sub-linear and super-linear cases are considered. 相似文献
12.
Giuseppe M. Coclite Gisèle R. Goldstein Jerome A. Goldstein 《Journal of Differential Equations》2009,246(6):2434-3971
Of concern is the nonlinear uniformly parabolic problem
13.
Fabio Cipriani 《Potential Analysis》1994,3(2):203-218
We give a general criterion for the intrinsic ultracontractivity of Dirichlet Laplacians –
D
on domainsD ofR
d d 3, based on the Lieb's formula. It applies to various classes of domains (e.g. John, Hölder andL
p-averaging domains) and gives new conditions for intrinsic ultracontractivity in terms of the Minkowski dimension of the boundary D. In particular, isotropic self-similar fractals and domains satisfying a c-covering condition are considered. 相似文献
14.
We prove a Harnack inequality for a degenerate parabolic equation using proper estimates based on a suitable version of the
Rayleigh quotient.
Dedicated to Giuseppe Da Prato on the occasion of his 70th birthday 相似文献
15.
Goro Akagi Kazumasa Suzuki 《Calculus of Variations and Partial Differential Equations》2008,31(4):457-471
The existence, uniqueness and regularity of viscosity solutions to the Cauchy–Dirichlet problem are proved for a degenerate
nonlinear parabolic equation of the form , where denotes the so-called infinity-Laplacian given by . To do so, a coercive regularization of the equation is introduced and barrier function arguments are also employed to verify
the equi-continuity of approximate solutions. Furthermore, the Cauchy problem is also studied by using the preceding results
on the Cauchy–Dirichlet problem.
Dedicated to the memory of our friend Kyoji Takaichi.
The research of the first author was partially supported by Waseda University Grant for Special Research Projects, #2004A-366. 相似文献
16.
Strong convergence theorems are obtained for a finite family of asymptotically nonexpansive mappings and semigroups by the modified Mann method. 相似文献
17.
We consider autonomous parabolic Dirichlet problems in a regular unbounded open set Ω⊂RN involving second-order operator A with (possibly) unbounded coefficients. We determine new conditions on the coefficients of A yielding global gradient estimates for the bounded classical solution. 相似文献
18.
Habtu Zegeye 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(1):325-329
Strong convergence theorems are obtained for a finite family of nonexpansive mappings and semigroups by the hybrid method. 相似文献
19.
Shota Sato 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(4):1383-1392
We consider the Cauchy problem for a parabolic partial differential equation with a power nonlinearity. Our concern in this paper is the existence of a singular solution with smooth initial data. By using the Haraux-Weissler equation, it is shown that there exist singular forward self-similar solutions. Using this result, we also obtain a sufficient condition for the singular solution with general initial data including smooth initial data. 相似文献