Electron. J. Differential Equations, Vol. 2020 (2020), No. 120, pp. 1-10.

Rothe's method for solving semi-linear differential equations with deviating arguments

Darshana Devi, Duranta Chutia, Rajib Haloi

Abstract:
We consider a semi-linear differential equation of parabolic type with deviating arguments in a Banach space with uniformly convex dual, and apply Rothe's method to establish the existence and uniqueness of a strong solution. We also include an example as an application of the main result.

Submitted October 23, 2020. Published December 10, 2020.
Math Subject Classifications: 34G20, 34K30, 35D35, 35K58.
Key Words: Strong solution; deviating argument; semigroup of bounded linear operators; semidiscretization method
DOI: 10.58997/ejde.2020.120

Show me the PDF file (294 KB), TEX file for this article.

Darshana Devi
Department of Mathematical Sciences
Tezpur University
Sonitpur, Assam, Pin 784028, India
email: darsana.mou@gmail.com
Duranta Chutia
Department of Mathematical Sciences
Tezpur University
Sonitpur, Assam, Pin 784028, India
email: durantachutia123@gmail.com
  Rajib Haloi
Department of Mathematical Sciences
Tezpur University, Sonitpur
Assam, Pin 784028, India
email: rajib.haloi@gmail.com, phone +913712-275511, fax +913712-267006

Return to the EJDE web page