{"product_id":"spectral-properties-and-stability-of-self-similar-wave-maps-linear-stability-of-co-rotational-solutions-von-roland-donninger","title":"Spectral Properties and Stability of Self-Similar Wave Maps","description":"\u003cp\u003eIn this thesis the Cauchy problem and in particular the question of singularity formation for co-rotational wave maps from Minkowski space to the three-sphere is studied. Numerics indicate that self-similar solutions play a crucial role in dynamical time evolution. In particular, it is conjectured that a certain solution f defines a universal blow up pattern in the sense that the future development of a large set of generic blow up initial data approaches f. Thus, singularity formation is closely related to stability properties of self-similar solutions. In this work, the problem of linear stability is studied by functional analytic methods. In particular, a complete spectral analysis of the perturbation operators is given and well-posedness of the linearized Cauchy problem is proved by means of semigroup theory and, alternatively, the functional calculus for self-adjoint operators. These results lead to growth estimates which provide information on the stability of self-similar wave maps. The thesis is intended to be self-contained, i.e. all the mathematical requirements are carefully introduced, including proofs for many results which could be found elsewhere.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783838101873\"\u003e\u003ch3\u003eLinear Stability of Co-rotational Solutions\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783838101873","offer_id":39456474497117,"sku":"9783838101873","price":69.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/b15b8541-0bf7-41c4-8540-9ed80f0c3054.jpg?v=1757741455","url":"https:\/\/shop.autorenwelt.de\/products\/spectral-properties-and-stability-of-self-similar-wave-maps-linear-stability-of-co-rotational-solutions-von-roland-donninger","provider":"Autorenwelt Shop","version":"1.0","type":"link"}