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PARTIAL DIFFERENTIAL EQUATIONS

PARTIAL DIFFERENTIAL EQUATIONSMath 124A Fall 2010 Viktor of MathematicsUniversity of California, Santa BarbaraThese lecture notes arose from the course PARTIAL DIFFERENTIAL EQUATIONS Math124A taught by the author in the Department of Mathematics at UCSB in the fallquarters of 2009 and 2010. The selection of topics and the order in which theyare introduced is based on [Str]. Most of the problems appearing in this text arealso borrowed from Strauss. A list of other references that were consulted whileteaching this course appears in the bibliography at the notes are copylefted, and may be freely used for noncommercial educationalpurposes. I will appreciate any and all feedback directed to the e-mail addresslisted above. The most up-to date version of these notes can be downloaded fromthe URL given - December 2010 ~ Classification of PDEs .. Examples.

x= u t+v t+(u+v)(u x+v x) = (u t+uu x)+(v t+vv x)+uv x+vu x6=Lu+Lv: You can check that the second condition of linearity fails as well. This happens precisely due to the nonlinearity of the uu x term, which is quadratic in \uand its derivatives". Notice that for a linear equation, if uis a solution, then so is cu, and if vis another solution, then

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