Skip to main content
SpringerLink
Log in

Evolution Equations

  • Chapter
  • First Online:
Problems on Partial Differential Equations

Part of the book series: Problem Books in Mathematics ((PBM))

  • 2942 Accesses

Abstract

This chapter deals with evolution equations, i.e., equations depending on a time variable. It begins with first order equations and the theory of characteristics. Then, the wave equation is introduced, leading to a systematic study of hyperbolic equations (Fourier transform methods and energy estimates). Finally, parabolic equations and the regularity of their weak solutions are investigated.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 69.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In fact we will only deal with such equations.

References

  1. S. Alinhac. Hyperbolic partial differential equations. Universitext. Springer, Dordrecht, 2009.

    Book  Google Scholar 

  2. L. C. Evans. Partial differential equations, volume 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, second edition, 2010.

    MATH  Google Scholar 

  3. F. John. Partial differential equations, volume 1 of Applied Mathematical Sciences. Springer-Verlag, New York, fourth edition, 1991.

    Google Scholar 

  4. E. H. Lieb and M. Loss. Analysis, volume 14 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, second edition, 2001.

    MATH  Google Scholar 

  5. G. M. Lieberman. Second order parabolic differential equations. World Scientific Publishing Co., Inc., River Edge, NJ, 1996.

    Book  Google Scholar 

  6. R. S. Strichartz. A guide to distribution theory and Fourier transforms. Reprint of the 1994 original. World Scientific Publishing Co., Inc., River Edge, NJ, 2003.

    Google Scholar 

  7. Z. Szmydt. Fourier transformation and linear differential equations. D. Reidel Publishing Co., Dordrecht-Boston, Mass.; PWN—Polish Scientific Publishers, Warsaw, revised edition, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. The University of Warsaw, Warsaw, Poland

    Maciej Borodzik, Paweł Goldstein, Piotr Rybka & Anna Zatorska-Goldstein

Authors
  1. Maciej Borodzik
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Paweł Goldstein
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Piotr Rybka
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Anna Zatorska-Goldstein
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Borodzik, M., Goldstein, P., Rybka, P., Zatorska-Goldstein, A. (2019). Evolution Equations. In: Problems on Partial Differential Equations. Problem Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-030-14734-1_5

Download citation

Publish with us

Policies and ethics

Search

Navigation