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The Neumann Problem for Parabolic Hessian Quotient Equations
Springer Science and Business Media LLC - Tập 37 - Trang 1313-1348 - 2021
In this paper, we consider the Neumann problem for parabolic Hessian quotient equations. We show that the k-admissible solution of the parabolic Hessian quotient equation exists for all time and converges to the smooth solution of elliptic Hessian quotient equations. Also solutions of the classical Neumann problem converge to a translating solution.
A fibration of categories overH B
Springer Science and Business Media LLC - Tập 13 - Trang 553-562 - 1997
K. A. Hardie and K. H. Kamps investigated the track homotopy categoryH
B over a fixed spaceB ([5]). This paper extendsH
B to the track homotopy categoryH
b over a fixed mapb:
$$B \to \bar B$$
, such that there exists a split fibration of categoriesL:H
......
Global Existence of Solutions for the Kawahara Equation in Sobolev Spaces of Negative Indices
Springer Science and Business Media LLC - Tập 23 - Trang 1435-1446 - 2007
We first prove that the Cauchy problem of the Kawahara equation,
$$
\partial _{t} u + u\partial _{x} u + \beta \partial ^{3}_{x} u + \gamma \partial ^{5}_{x} u = 0
$$
, is locally solvable if the initial data belong to H
r
(R) and
......
Homological dimensions of the extension algebras of monomial algebras
Springer Science and Business Media LLC - Tập 31 - Trang 675-694 - 2015
The main objective of this paper is to study the dimension trees and further the homological dimensions of the extension algebras — dual and trivially twisted extensions — with a unified combinatorial approach using the two combinatorial algorithms — Topdown and Bottomup. We first present a more complete and clearer picture of a dimension tree, with which we are then able, on the one hand, to shar......
Relative left derived functors of tensor product functors
Springer Science and Business Media LLC - Tập 32 - Trang 753-764 - 2016
We introduce and study the relative left derived functor Tor
n
(F,F′)(−,−) in the module category, which unifies several related left derived functors. Then we give some criteria for computing the F-resolution dimensions of modules in terms of the properties of TorTor
n
......
Classification of Hardy Submodules and Characteristic Space Theory (A Brief and Selective Survey)
Springer Science and Business Media LLC - Tập 19 - Trang 513-522 - 2003
This paper is a brief and selective survey on classification of Hardy Submodules over the polydisk. The survey reports some progress in classification of Hardy submodules
Long-term analysis of degenerate parabolic equations in ℝ N
Springer Science and Business Media LLC - Tập 31 - Trang 383-410 - 2015
Longtime behavior of degenerate equations with the nonlinearity of polynomial growth of arbitrary order on the whole space ℝ
N
is considered. By using ℓ-trajectories methods, we proved that weak solutions generated by degenerate equations possess an (L
2
......
Higher Genus FJRW Theory for Fermat Cubic Singularity
Springer Science and Business Media LLC - Tập 37 - Trang 1179-1204 - 2021
In this paper, we study the higher genus FJRW theory of Fermat cubic singularity with maximal group of diagonal symmetries using Givental formalism. As results, we prove the finite generation property and holomorphic anomaly equation for the associated FJRW theory. Via general LG-LG mirror theorem, our results also hold for the Saito-Givental theory of the Fermat cubic singularity.
Periodic Solutions of a Class of Second Order Functional Differential Equations
Springer Science and Business Media LLC - - 2005
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