Perspectives in nonlinear diffusion: between analysis, physics and geometry
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Title 
Perspectives in nonlinear diffusion: between analysis, physics and geometry

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Number of Parts 
33

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CC Attribution 3.0 Germany:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
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Release Date 
2006

Language 
English

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Subject Area  
Abstract 
We review some topics in the mathematical theory of nonlinear diffusion. Attention is focused on the porous medium equation and the fast diffusion equation, including logarithmic diffusion. Special features are the existence of free boundaries, the limited regularity of the solutions and the peculiar asymptotic laws for porous medium flows, while for fast diffusions we find the phenomena of finitetime extinction, delayed regularization, nonuniqueness and instantaneous extinction. Logarithmic diffusion with its strong geometrical flavor is also discussed. Connections with functional analysis, semigroup theory, physics of continuous media, probability and differential geometry are underlined.

Keywords  nonlinear diffusion degenerate parabolic equations flows in porous media 
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40:39
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49:25
And the whole thing is continuing in their last in this really is what I love To that the role Laura thinking dimension is what there is the the newest The dimensions the system as a friend and a new did his duty food dissipation tested did we got on onto the Andes is really what the punch line at nite Distorting you for diners is bond there's no matter what You at depots in your only to Usually and eh
50:04
Our which is a scathing so that the water is lost The relation between A lot of functional analysis what it is That what it is that nobody what it is is 1 of the driving forces of year and it needed now that it has done with those now did disabled there is no 1 on but this Not so we think that something better we were trying to get test which is buoyed like a the the Wash Obtain what few years which is universally viewed take the press which is you don't mind has retained the place is mother alone now is believe it or not is a manifestation of the cycle of And mystique is because of farm borrowers with Janice But it has allowed cover earlier statement approved by the main results nature tool which is this Dad Solution of these problems have we see on the judging Nice for wish and the interface is Which is And then we will find a nite rules Did you by stating the states then you Not only did just that I wish I knew immediately what it is it is that they Does Move that These days the so that if required but size the food is moving all of a sudden and then I moved up a year in my day at the beginning of It will also Taylor states do Part following faces he let him not to show that I'm add
52:02
Their faces were destroyed by any language moved over his beautiful part of the city that event did would much Time to talk about it but let me tell you that Wang Chung Ju get half places of writing interface with stable Stretched and and is on the point and you don't have a lift interface which is very high and you don't have any interface Which collide here with a set the ball figure would have been in isolated Boeing which is meant as they
52:42
And what we proved 1887 with no advance but site is that after Find a solution that will modify leaving 7 inches is And we were stopped for a 4th day India's with no can't do better and then cut off Rolled he's behind a hand It was not 160 pages and you lose Stand Monaghan and to prove that they basis and that he did this stumbling block was going from C 1 to see light because the junta diseases tho the perimeter so that went all the way back in then you get better support and ahead amenities Then he never bothered to use scissors he said it was too long it was overly that with some of the pressure with wonderful work it doesn't get much about publishing what kind of PC Nam I will you John did Did he got a taste of the with callers because it 1 I wanted to their the lenient sentence theater which is something half Dead before being chosen may I choose as they a to show broader with to science dignity palatial After writing would do Signed solutions will divorce can be found the time being called in my day combined last due to initial data and a force and here's the theater was removed from 1st But denying partially and the whole of the south And said that in mind that is the same with these Asymptotic class and just as you and the matter is being that different most disease after a modified by that exponent of these that is a reach juicy the zone boast to Cedars must be in vain been the missing days thinking 0 a B Space but did that really is why people In these so I'd say is that air was not post is due out there Door functions You should judge of believed did you got because go say what and they know but most of the dead and I had to write its own survive and lower Both you want 3 might have been lost The we found idea and improve the carriers with Not public support Is among Zito solutions boss area no investigation of son We buy ruled that generated not being ruled this Arrange due to their boast zeal that dose of rules there Don't blow due date now Is black but remember the collapse of the school has But So do that then don't be center But only if ends But And then let these few years old and it is very fast commercial bank You the distance the goal is to do what we don't know how but it's a very I know most of and was This is Set up and Energy flows the lending now right 2 days Show how this evil because people like pictures in my collaborate The Charles later allowed to have This Thursday It with thoughtful Still I that would do it again Appeal of the guards is Thanks to vote was doing good work in action of so that we don't know about that A after these leaders fearing you would do no ball And that And they got wasn't under the Barcelona Art wrote a beautiful but with GE's at 1st found it does not get through them that way But rights of U.S. Steel the yard visual has has Funny but their value our Rule that you don't get bound on the moment together a they know we have been working for years The initial rates and it's not just me and they might French GM show and I said I wanted to know something about dependent on the battered and would reduce the result they find beautiful art if you don't take your pressure as you do in my life which is kind of a physical quantity and did did taste and that there is made with I want to be a duel between our my eyes But not to posters and since Steve Is there Correct would do say is not going to the bottom of 5 Julie done really But not all of these is the release of the sick of the people that what it is now I didn't give details of all us like dinosaurs so that now Those less then they can't find rights which I Beautiful views of what has been done in last year's you'll have to to release which is buying another man I the size and is that by which The dual normalization is very poorly on any major defined as certain Funchal have reduced VAT sound dead out of some the most money and Lecture about how these funds But this just a standard functionality and they make it don't that we did say that he thought his and Nannette mainly most dissipation and ended Daisy based on goes down with the right And finally Delaware is proportional dissipation to doing that ideas which gives you exponential decay you don't exponential decay he called a cell He declares exponentially and this is set up So he chased our time indeed that's it And that beautiful day stay alive for a girl so that gives them just as the computations we did they leave it to gain courtesy of that you'll see back dying
1:00:46
These elections in these days each 5 Monday today's a class tool punched and after why it's about a Ignatius goes down because of defect That means that that didn't do this and see what he did but he declares the bears showed fund there is off so these rules We don't want gravity for he after 5 times in new result Through proved your most of which now is the fast diffusion of glacial we did that religion and juicy is bad for that You know which is assisting us lose Look prove that it is That now Still on dog tags agenda In the end that they got it is the thing because full of pure mathematics have take the title of writing a study of my life these people with beautiful minds in a book that will be sold in March The Paris a sushi pages of conclusion but If you don't want to fall so that you want to call for more advanced topics of his I wrote another book ready here and I would find Oxford University there's still what of these comfortable with wedding Then he noticed billion dollars is moving indicators usually want to know they are not all of the leaders of these is within sight of the wild 2 years ago Dr. became for the part of the whole went OK so it that Don't About 30 Set of is that people are doing now and just that with that 1 of the least of the future is begun in probabilistic with busses Rules there is viewed by VA let me on studies of defamation of transportation which is like those of us in the kitchens and He found a new kind of Stanley says In other people have been working group contact for the 1st these differed busses tying the knot The new job that I would tell you that That But is constitutional with emulators want but that's it is 1 of the city's center here is not the 1 I told you that And compared to my books will Ah but wanted assistance for an individual in the world that's all you want to do now Parabolic waste and that is what might cost having your even while the coverups of a minivan and you want abroad in the Union division units process is a bad thing you have the will of the voters was not the way use which is the the elaboration and maybe you have built but initial wage Which was described These Sanchez villages and So what is now I don't I of course I'm dead beauties of the future but jazz Last nite I would tell you that the obligation to jump Saying you likely to make sure these evolution where Paula Mile representation of surface DSS where you will be honest where they stand according to have a unit in future when she would use of mobile we and they it with that dog sometimes pressed the 1st CD is that this is A diffusely West but has It is up to the beginning of this show you make it devoting dying in the whole place Lucy's for by Julie of last due time and there is no way you can avoid so they sound says happy that that you don't discovered with fists if you do John Anthony is house so the mentions John they at The usually outlook on the on intefadeh views in case it is connected with this Not future which is a regional social model and of Or so I don't want to do a picture of how must not It is the picture of your days that usually glacial for a while but nobody has pulled down a lot less fat They but few approach is causing defiant days down sold They said Looks like it that increases is for By the time it is what we are doing so somebody for my daughter of the newly minted usually problems Betty Siegel Feces and represent a water on pure mathematics essentially but Italy which of functional analysis with go deeper With John Hagerty if you don't have to do but it throws a partial was probably From devices said there had been no only said the museums and I think I've stopped here I think you very much for your attention