Matches in SemOpenAlex for { <https://semopenalex.org/work/W1978467820> ?p ?o ?g. }
Showing items 1 to 84 of
84
with 100 items per page.
- W1978467820 abstract "In this paper we determine exact, analytical solutions of the parabolic, nonlinear diffusion equation θ t = (f 2 (θ)θ x ) x + f 1 (θ), in which we insist that at least one of f 1 and f 2 is arbitrary. To do this we find reductions of the equation using a method based on the Clarkson and Kruskal direct method (Clarkson & Kruskal, 1989, J. Math. Phys., 30 2201-2213). A modification to the 'algorithm' used and a generalization of the ansatz with which one begins are necessary. Clarkson (1995) states that 'it is not clear how the direct method... may be applied to equations which contain arbitrary functions [of the dependent variable]'. Here we show how this can be accomplished by a modification of the algorithm used. We also consider a more general ansatz in which the new independent variable depends not only on the given independent variables but also on the given dependent variable. Whilst this principle is now well known, to the author's knowledge, how this is done in practice has not been explicitly described, nor have any results determined from this generalized ansatz previously been reported. Finally we consider an ansatz which is equivalent to a combination of a hodograph transformation and the usual reduction. In each of the three cases we find new reductions in which f 2 remains arbitrary and f 1 is given in terms of f 2 . The first and third cases are of particular interest: for each, a large class of new reductions and solutions are found." @default.
- W1978467820 created "2016-06-24" @default.
- W1978467820 creator A5050518220 @default.
- W1978467820 date "2000-06-01" @default.
- W1978467820 modified "2023-09-28" @default.
- W1978467820 title "On direct, implicit reductions of a nonlinear diffusion equation with an arbitrary function - generalizations of Clarkson's and Kruskal's method" @default.
- W1978467820 doi "https://doi.org/10.1093/imamat/64.3.223" @default.
- W1978467820 hasPublicationYear "2000" @default.
- W1978467820 type Work @default.
- W1978467820 sameAs 1978467820 @default.
- W1978467820 citedByCount "17" @default.
- W1978467820 countsByYear W19784678202013 @default.
- W1978467820 countsByYear W19784678202015 @default.
- W1978467820 countsByYear W19784678202017 @default.
- W1978467820 countsByYear W19784678202019 @default.
- W1978467820 countsByYear W19784678202020 @default.
- W1978467820 countsByYear W19784678202022 @default.
- W1978467820 crossrefType "journal-article" @default.
- W1978467820 hasAuthorship W1978467820A5050518220 @default.
- W1978467820 hasConcept C111335779 @default.
- W1978467820 hasConcept C114614502 @default.
- W1978467820 hasConcept C121332964 @default.
- W1978467820 hasConcept C130979935 @default.
- W1978467820 hasConcept C134306372 @default.
- W1978467820 hasConcept C14036430 @default.
- W1978467820 hasConcept C158622935 @default.
- W1978467820 hasConcept C177148314 @default.
- W1978467820 hasConcept C182365436 @default.
- W1978467820 hasConcept C197766306 @default.
- W1978467820 hasConcept C2524010 @default.
- W1978467820 hasConcept C28826006 @default.
- W1978467820 hasConcept C33923547 @default.
- W1978467820 hasConcept C37914503 @default.
- W1978467820 hasConcept C62520636 @default.
- W1978467820 hasConcept C63645285 @default.
- W1978467820 hasConcept C64331007 @default.
- W1978467820 hasConcept C78458016 @default.
- W1978467820 hasConcept C86803240 @default.
- W1978467820 hasConceptScore W1978467820C111335779 @default.
- W1978467820 hasConceptScore W1978467820C114614502 @default.
- W1978467820 hasConceptScore W1978467820C121332964 @default.
- W1978467820 hasConceptScore W1978467820C130979935 @default.
- W1978467820 hasConceptScore W1978467820C134306372 @default.
- W1978467820 hasConceptScore W1978467820C14036430 @default.
- W1978467820 hasConceptScore W1978467820C158622935 @default.
- W1978467820 hasConceptScore W1978467820C177148314 @default.
- W1978467820 hasConceptScore W1978467820C182365436 @default.
- W1978467820 hasConceptScore W1978467820C197766306 @default.
- W1978467820 hasConceptScore W1978467820C2524010 @default.
- W1978467820 hasConceptScore W1978467820C28826006 @default.
- W1978467820 hasConceptScore W1978467820C33923547 @default.
- W1978467820 hasConceptScore W1978467820C37914503 @default.
- W1978467820 hasConceptScore W1978467820C62520636 @default.
- W1978467820 hasConceptScore W1978467820C63645285 @default.
- W1978467820 hasConceptScore W1978467820C64331007 @default.
- W1978467820 hasConceptScore W1978467820C78458016 @default.
- W1978467820 hasConceptScore W1978467820C86803240 @default.
- W1978467820 hasLocation W19784678201 @default.
- W1978467820 hasOpenAccess W1978467820 @default.
- W1978467820 hasPrimaryLocation W19784678201 @default.
- W1978467820 hasRelatedWork W1981004216 @default.
- W1978467820 hasRelatedWork W1985167223 @default.
- W1978467820 hasRelatedWork W1985327281 @default.
- W1978467820 hasRelatedWork W1989975146 @default.
- W1978467820 hasRelatedWork W1994083734 @default.
- W1978467820 hasRelatedWork W2004508862 @default.
- W1978467820 hasRelatedWork W2014454023 @default.
- W1978467820 hasRelatedWork W2022505251 @default.
- W1978467820 hasRelatedWork W2033289717 @default.
- W1978467820 hasRelatedWork W2045818435 @default.
- W1978467820 hasRelatedWork W2046601112 @default.
- W1978467820 hasRelatedWork W2050596297 @default.
- W1978467820 hasRelatedWork W2058417928 @default.
- W1978467820 hasRelatedWork W2061396765 @default.
- W1978467820 hasRelatedWork W2094366276 @default.
- W1978467820 hasRelatedWork W2138480278 @default.
- W1978467820 hasRelatedWork W2147635720 @default.
- W1978467820 hasRelatedWork W2157482348 @default.
- W1978467820 hasRelatedWork W2162537074 @default.
- W1978467820 hasRelatedWork W3106104040 @default.
- W1978467820 isParatext "false" @default.
- W1978467820 isRetracted "false" @default.
- W1978467820 magId "1978467820" @default.
- W1978467820 workType "article" @default.