Consider the following system Ut – (u?)ąż = 0, u > 0, X ER, t> 0 with the following conditions Ux(t,0) = 0, lim u= 0, 22

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Consider The Following System Ut U Az 0 U 0 X Er T 0 With The Following Conditions Ux T 0 0 Lim U 0 22 1 (105.38 KiB) Viewed 64 times

Consider the following system Ut – (u?)ąż = 0, u > 0, X ER, t> 0 with the following conditions Ux(t,0) = 0, lim u= 0, 22700 u(t, x) dx = 1 ~ (a) What is the Order of the above equation? Is it linear or non-linear? Is it homogeneous or non- homogeneous? (b) Guess a solution of the form u(t, x) = -f(n) where n xt-ß. Use chain rule to determine the values of a and B which reduce the equation to = (254+) - - 0 (c) Solve this equation and determine u(t, x). Hint: u(t, x) is a piecewise continuous function. (d) Sketch the solution when t =1,2,3.