Matches in SemOpenAlex for { <https://semopenalex.org/work/W2997132156> ?p ?o ?g. }
Showing items 1 to 67 of
67
with 100 items per page.
- W2997132156 endingPage "54" @default.
- W2997132156 startingPage "47" @default.
- W2997132156 abstract "The purpose of this work is to build the heat equation in a space with finite variant measure, using the concept of divergence with respect to a measure, to get a solution of the initial vaule problem for some partial cases as well as the general fundamental solution, to prove uniqueness and existence of the solution of the corresponding initial value problem, to analyse the conditions the solution of the initial value problem exists and is unique under. The solutions for two partial cases are obtained by means of Fourier transformation, whereas general solution is obtained via the parametrix technique. The measure $mu$ that is used in this work is considered as positive absolutely continuous w.r.t invariant Lebesgue measure, and its Radon–Nikodym derivative is piecewise smooth and is bounded with its first derivative on $mathbb{R}^n$. If a vector field $vb{Z}$ is smooth on $mathbb{R}^n$, then $mu$ is differentiable along $vb{Z}$, and its logarithmic derivative along $vb{Z}$ is denoted as $dive_mu vb{Z}$. In this case Laplace operator is introduced on $C^2_b(mathbb{R}^n)$ as $Delta u = dive_mu ( grnvect u$), and thereby we can set standard Cauchy problem for heat equation: $ begin{cases}dfrac{partial u}{partial{t}}=Delta u; u(x,0)=varphi(x), end{cases},$ which is to be solved by means of aforementioned methods." @default.
- W2997132156 created "2020-01-10" @default.
- W2997132156 creator A5088829721 @default.
- W2997132156 date "2018-12-03" @default.
- W2997132156 modified "2023-09-25" @default.
- W2997132156 title "Cauchy problem for the heat equation with Laplacian with respect to a measure" @default.
- W2997132156 doi "https://doi.org/10.20535/mmtu-2018.1-047" @default.
- W2997132156 hasPublicationYear "2018" @default.
- W2997132156 type Work @default.
- W2997132156 sameAs 2997132156 @default.
- W2997132156 citedByCount "0" @default.
- W2997132156 crossrefType "journal-article" @default.
- W2997132156 hasAuthorship W2997132156A5088829721 @default.
- W2997132156 hasBestOaLocation W29971321561 @default.
- W2997132156 hasConcept C118733216 @default.
- W2997132156 hasConcept C134306372 @default.
- W2997132156 hasConcept C14158598 @default.
- W2997132156 hasConcept C153635880 @default.
- W2997132156 hasConcept C165700671 @default.
- W2997132156 hasConcept C202444582 @default.
- W2997132156 hasConcept C202787564 @default.
- W2997132156 hasConcept C26955809 @default.
- W2997132156 hasConcept C2777021972 @default.
- W2997132156 hasConcept C2777105136 @default.
- W2997132156 hasConcept C2780009758 @default.
- W2997132156 hasConcept C33923547 @default.
- W2997132156 hasConcept C34388435 @default.
- W2997132156 hasConcept C41008148 @default.
- W2997132156 hasConcept C77088390 @default.
- W2997132156 hasConcept C93779851 @default.
- W2997132156 hasConceptScore W2997132156C118733216 @default.
- W2997132156 hasConceptScore W2997132156C134306372 @default.
- W2997132156 hasConceptScore W2997132156C14158598 @default.
- W2997132156 hasConceptScore W2997132156C153635880 @default.
- W2997132156 hasConceptScore W2997132156C165700671 @default.
- W2997132156 hasConceptScore W2997132156C202444582 @default.
- W2997132156 hasConceptScore W2997132156C202787564 @default.
- W2997132156 hasConceptScore W2997132156C26955809 @default.
- W2997132156 hasConceptScore W2997132156C2777021972 @default.
- W2997132156 hasConceptScore W2997132156C2777105136 @default.
- W2997132156 hasConceptScore W2997132156C2780009758 @default.
- W2997132156 hasConceptScore W2997132156C33923547 @default.
- W2997132156 hasConceptScore W2997132156C34388435 @default.
- W2997132156 hasConceptScore W2997132156C41008148 @default.
- W2997132156 hasConceptScore W2997132156C77088390 @default.
- W2997132156 hasConceptScore W2997132156C93779851 @default.
- W2997132156 hasIssue "1" @default.
- W2997132156 hasLocation W29971321561 @default.
- W2997132156 hasOpenAccess W2997132156 @default.
- W2997132156 hasPrimaryLocation W29971321561 @default.
- W2997132156 hasRelatedWork W1981565441 @default.
- W2997132156 hasRelatedWork W1999585122 @default.
- W2997132156 hasRelatedWork W2019936573 @default.
- W2997132156 hasRelatedWork W2066078240 @default.
- W2997132156 hasRelatedWork W2149537351 @default.
- W2997132156 hasRelatedWork W2150570786 @default.
- W2997132156 hasRelatedWork W2380363875 @default.
- W2997132156 hasRelatedWork W2986365298 @default.
- W2997132156 hasRelatedWork W4281264102 @default.
- W2997132156 hasRelatedWork W4304013826 @default.
- W2997132156 hasVolume "2018" @default.
- W2997132156 isParatext "false" @default.
- W2997132156 isRetracted "false" @default.
- W2997132156 magId "2997132156" @default.
- W2997132156 workType "article" @default.