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On the Stability of Type I Blow Up for the Energy Super Critical Heat Equation

Charles Collot
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      The authors consider the energy super critical semilinear heat equation $\partial {t}u=\Delta u u^{p}, x\in \mathbb{R}^3, p>5.$ The authors first revisit the construction of radially symmetric self similar solutions performed through an ode approach and propose a bifurcation type argument which allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. They then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional nonradial stability of these solutions for smooth well localized initial data using energy bounds. The whole scheme draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.
      Format: Paperback / softback CONTRIBUTORS: Charles Collot EAN: 9781470436261 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2019-10-01 CITY: GENRE: MATHEMATICS / Differential Equations / General WIDTH: 178 cm SPINE:

      Book Themes:

      Differential calculus and equations

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      Charles Collot, Universite de Nice-Sophia Antipolis, France.Pierre Raphael, Universite de Nice-Sophia Antipolis, France.Jeremie Szeftel, Universite Paris 6, France.
      The authors consider the energy super critical semilinear heat equation $\partial {t}u=\Delta u u^{p}, x\in \mathbb{R}^3, p>5.$ The authors first revisit the construction of radially symmetric self similar solutions performed through an ode approach and propose a bifurcation type argument which allows for a sharp control of the spectrum of the corresponding linearized operator in suitable weighted spaces. They then show how the sole knowledge of this spectral gap in weighted spaces implies the finite codimensional nonradial stability of these solutions for smooth well localized initial data using energy bounds. The whole scheme draws a route map for the derivation of the existence and stability of self-similar blow up in nonradial energy super critical settings.
      Format: Paperback / softback CONTRIBUTORS: Charles Collot EAN: 9781470436261 COUNTRY: United States PAGES: WEIGHT: 0 g HEIGHT: 254 cm
      PUBLISHED BY: American Mathematical Society DATE PUBLISHED: 2019-10-01 CITY: GENRE: MATHEMATICS / Differential Equations / General WIDTH: 178 cm SPINE:

      Book Themes:

      Differential calculus and equations

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      Charles Collot, Universite de Nice-Sophia Antipolis, France.Pierre Raphael, Universite de Nice-Sophia Antipolis, France.Jeremie Szeftel, Universite Paris 6, France.

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