Brief survey of computer assisted proofs for partial differential equations
Brief survey of computer assisted proofs for partial differential equations
ÌýI will present a brief survey of computer assisted methodsÌýof studying partial differential equations that I have workedÌýon. The methods I am going to discuss allow for obtaining proofsÌýof the existence of particular solutions of a certain class of PDEsÌýin a prescribed range of parameters. ÌýI will discuss opportunitiesÌý and limitations of the presentedÌýapproach. In particular most of the presented results have not beenÌýobtained using known techniques of 'classical analysis'. ÌýI will focus on two particular examples from my research, namelyÌý1)Ìýa proof of the existence of globally attracting solutions forÌýthe 1d viscous Burgers equation (with non-autonomous forcing)Ìý, andÌý2)Ìýrecent proof of the heteroclinic connections in theÌý1d Ohta-Kawasaki (diblock copolymers) modelÌý