Solvability and completeness of solutions of parabolic differential-operator equations [PDF]
Математичні Студії, 2011 We consider an abstract Cauchy problem for parabolic differential-operator equations in Hilbert spaces. Initial boundary value problems for parabolic equations are reduced to the Cauchy problem for a system of parabolic differential equations.
M. M. Mamedov
doaj
Regularity Analysis for an Abstract System of Coupled Hyperbolic and Parabolic Equations [PDF]
, 2014 In this paper, we provide a complete regularity analysis for an abstract system of coupled hyperbolic and parabolic equations in a complex Hilbert space.
Hao, Jianghao +2 more
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Embedding Operators in Vector-Valued Weighted Besov Spaces and Applications
Journal of Function Spaces and Applications, 2012 The embedding theorems in weighted Besov-Lions type spaces 𝐵𝑙,𝑠𝑝,𝑞,𝛾 (Ω;𝐸0,𝐸) in which 𝐸0,𝐸 are two Banach spaces and 𝐸0⊂𝐸 are studied. The most regular class of interpolation space 𝐸𝛼 between 𝐸0 and E is found such that the mixed differential operator ...
Veli Shakhmurov
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Doubly nonlinear evolution equation associated with elliptic-parabolic free boundary problems [PDF]
, 2004 We study an abstract doubly nonlinear evolution equations associated with elliptic-parabolic free boundary problems. In this paper we show the existence and uniqueness of solution for the doubly nonlinear evolution equation.
Yamazaki, Noriaki
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Analysis of black hole solutions in parabolic class using neural networks
European Physical Journal C: Particles and Fields, 2023 In this paper, we introduce a numerical method based on Artificial Neural Networks (ANNs) for the analysis of black hole solutions to the Einstein-axion-dilaton system in a high dimensional parabolic class.
Ehsan Hatefi +2 more
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An abstract framework for parabolic PDEs on evolving spaces
, 2015 We present an abstract framework for treating the theory of well-posedness of solutions to abstract parabolic partial differential equations on evolving Hilbert spaces.
Alphonse, Amal +2 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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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.
openaire +1 more source
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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First derivatives estimates for finite-difference schemes [PDF]
, 2008 . We give sufficient conditions under which solutions of discretized in space second-order parabolic and elliptic equations, perhaps degenerate, admit estimates of the first derivatives in the space variables independent of the mesh size ...
Gyongy, Istvan, Krylov, Nicolai
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