View source for Hadamard's method of descent

{{Redirect-distinguish|Method of descent|Proof by infinite descent}}

In [[mathematics]], the '''method of descent''' is the term coined by the French [[mathematician]] [[Jacques Hadamard]] as a method for solving a [[partial differential equation]] in several [[Function of a real variable|real]] or [[complex variable]]s, by regarding it as the specialisation of an equation in more variables, constant in the extra parameters. This method has been used to solve the [[wave equation]], the [[heat equation]] and other versions of the [[Cauchy initial value problem]].

As {{harvtxt|Hadamard|1923}} wrote:

{{cquote|We thus have a first example of what I shall call a 'method of descent'. Creating a phrase for an idea which is merely childish and has been used since the first steps of the theory is, I must confess, rather ambitious; but we shall come across it rather frequently, so that it will be convenient to have a word to denote it. It consists in noticing that he who can do more can do less: if we can integrate equations with ''m'' variables, we can do the same for equations with (''m''&nbsp;–&nbsp;1) variables.}}

==References==
*{{citation|title=Lectures on Cauchy's Problem in Linear Partial Differential Equations|publisher= [[Dover Publications]]|year= 1923|isbn=0486495493|first=Jacques|last=Hadamard|authorlink=Jacques Hadamard|page=49}}
*{{citation|title=Partial differential equations|first1=Lipman|last1= Bers|authorlink1=Lipman Bers|first2= Fritz|last2= John|authorlink2=Fritz John|first3=Martin |last3=Schechter|publisher= [[American Mathematical Society]]|year= 1964|
isbn=0821800493|page=16}}
*{{citation|title=Methods of mathematical physics, Vol. II|first=Richard |last=Courant|authorlink=Richard Courant|first2=David|last2= Hilbert|authorlink2=David Hilbert|publisher=Interscience|year= 1953|page=205}}
*{{citation|title=Introduction to partial differential equations|first=Gerald B.|last= Folland|publisher=[[Princeton University Press]]|year= 1995|
page =171|isbn=0691043612}}
*{{citation|title=Jacques Hadamard: a universal mathematician|first=V. G.|last= Maz'ya|first2=  T. O.|last2= Shaposhnikova|publisher=American Mathematical Society|year=1998|page=472|isbn=0821819232}}


[[Category:Partial differential equations]]


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