Analytic Methods In The Theory Of Differential And Pseudo-Differential Equations Of Parabolic Type

1. Front Matter

   Pages i-ix

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2. Equations. Problems. Results. Methods. Examples

   • Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen

   Pages 1-52

3. Parabolic Equations of a Quasi-Homogeneous Structure

   • Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen

   Pages 53-175

4. Degenerate Equations of the Kolmogorov Type

   • Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen

   Pages 177-264

5. Pseudo-Differential Parabolic Equations with Quasi-Homogeneous Symbols

   • Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen

   Pages 265-319

6. Fractional Diffusion Equations

   • Samuil D. Eidelman, Anatoly N. Kochubei, Stepan D. Ivasyshen

   Pages 321-361

7. Back Matter

   Pages 363-390

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The theory of parabolic equations, a well-developed part of the contemporary partial differential equations and mathematical physics, is the subject theory of of an immense research activity. A continuing interest in parabolic equations is caused both by the depth and complexity of mathematical problems emerging here, and by its importance in specific applied problems of natural science, technology, and economics. This book aims at a consistent and, as far as possible, a complete exposition of analytic methods of constructing, investigating, and using fundamental solutions of the Cauchy problem for the following four classes of linear parabolic equations with coefficients depending on all variables: -7 E : 2b-parabolic partial differential equations (parabolic equations of a qua- l homogeneous structure), in which every spatial variable may have its own to the time variable. weight with respect E : degenerate partial differential equations of Kolmogorov's structure, which 2 generalize classical Kolmogorov equations of diffusion with inertia. E3: pseudo-differential equations with non-smooth quasi-homogeneous symbols. E : fractional diffusion equations. 4 These classes of equations generalize in various directions the classical equations and systems parabolic in the Petrovsky sense, which were defined in [180] and studied in a number of monographs [83, 45, 146, 107, 76] and survey articles [102, 1, 215, 70, 46].

• Cauchy problem
• Parabolic equations
• Pseudo-differential equations
• complexity
• differential equation
• diffusion
• mathematical physics
• partial differential equation
• solution
• partial differential equations

• Institute of Mathematics, National Academy of Sciences of Ukraine, Kiev, Ukraine

  Samuil D. Eidelman, Anatoly N. Kochubei

• Department of Mathematical Physics, National Technical University of Ukraine Kiev Polytechnical Institute, Kiev, Ukraine

  Stepan D. Ivasyshen

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