Abstract quasilinear parabolic equations
Mathematische Annalen, 1984 The author deals with an abstract quasilinear parabolic problem \(u'(t)=A(t,u(t))u(t)+f(t,u(t)), t>0\), \(u(0)=u_ 0\) in a Banach space X. His theorems on existence and uniqueness are such that a concrete quasilinear parabolic problem can be attacked without imposing growth conditions on the coefficients.
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Local regularity for fractional heat equations
, 2017 We prove the maximal local regularity of weak solutions to the parabolic problem associated with the fractional Laplacian with homogeneous Dirichlet boundary conditions on an arbitrary bounded open set $\Omega\subset\mathbb{R}^N$.
D Lamberton +16 more
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A posteriori error estimates for fully discrete fractional-step ϑ-approximations for parabolic equations [PDF]
, 2015 This is a pre-copyedited, author-produced PDF of an article accepted for publication in IMA Journal of Numerical Analysis following peer review. The version of record A posteriori error estimates for fully discrete fractional-step ϑ-approximations for ...
Akrivis +4 more
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On classification and invariants of second order non-parabolic linear partial differential equations in two variables [PDF]
, 2017 The paper deals with second order abstract linear partial differential equations (LPDE) over a partial differential field with two commuting differential operators.
Bekbaev, U.
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Feedback control for an abstract parabolic equation [PDF]
, 1987 Abstract : In their previous paper, the authors considered the problem of the exponential stabilization of the heat equation with Neumann boundary conditions in the smooth and bounded domain OMEGA in R(exp n), where partial derivative/partial derivative nu denotes the differentiation in the direction normal to the boundary partial derivative OMEGA. The
Rouben Rostamian +2 more
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Global existence of mild solutions for impulsive $ \psi- $Caputo fractional parabolic equations
Electronic Research ArchiveThis paper investigated a class of nonlinear $ \psi- $Caputo fractional parabolic equations with impulsive. We reformulated the fractional parabolic equations into abstract evolution equations.
Yonghong Ding, Yongxiang Li
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First-Order Regular and Degenerate Identification Differential Problems
Abstract and Applied Analysis, 2015 We are concerned with both regular and degenerate first-order identification problems related to systems of differential equations of weakly parabolic type in Banach spaces. Several applications to partial differential equations and systems will be given
A. Favini, A. Lorenzi, H. Tanabe
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A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem
Journal of Inequalities and Applications, 2018 In this paper, we investigate the spectral approximation of optimal control problem governed by nonlinear parabolic equations. A spectral approximation scheme for the nonlinear parabolic optimal control problem is presented. We construct a fully discrete
Lin Li +4 more
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Moving planes and sliding methods for fractional elliptic and parabolic equations
Advanced Nonlinear StudiesIn this paper, we summarize some of the recent developments in the area of fractional elliptic and parabolic equations with focus on how to apply the sliding method and the method of moving planes to obtain qualitative properties of solutions.
Wenxiong Chen, Yeyao Hu, Lingwei Ma
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Mixed problems for degenerate abstract parabolic equations and applications [PDF]
, 2017 Degenerate abstract parabolic equations with variable coefficients are studied. Here the boundary conditions are nonlocal. The maximal regularity properties of solutions for elliptic and parabolic problems and Strichartz type estimates in mixed $L_{p ...
Sahmurova, Aida, Shakhmurov, Veli
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