Maximal regularity for parabolic initial-boundary value problems in Sobolev spaces

1991 ◽  
Vol 208 (1) ◽  
pp. 297-308 ◽  
Author(s):  
Giovanni Dore ◽  
Alberto Venni
Keyword(s):  
Boundary Value Problems ◽  
Sobolev Spaces ◽  
Maximal Regularity ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Initial Boundary Value

scholarly journals Maximal regular boundary value problems in Banach-valued function spaces and applications

2006 ◽  
Vol 2006 ◽  
pp. 1-26 ◽  
Author(s):  
Veli B. Shakhmurov
Keyword(s):  
Boundary Value Problems ◽  
Differential Operators ◽  
Maximal Regularity ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Initial Boundary ◽  
Cylindrical Domain ◽  
Initial Boundary Value Problems ◽  
Nonlocal Boundary Value Problems ◽  
Initial Boundary Value

The nonlocal boundary value problems for differential operator equations of second order with dependent coefficients are studied. The principal parts of the differential operators generated by these problems are non-selfadjoint. Several conditions for the maximal regularity and the Fredholmness in Banach-valuedLp-spaces of these problems are given. By using these results, the maximal regularity of parabolic nonlocal initial boundary value problems is shown. In applications, the nonlocal boundary value problems for quasi elliptic partial differential equations, nonlocal initial boundary value problems for parabolic equations, and their systems on cylindrical domain are studied.

scholarly journals On degenerate Kirchhoff-type problems with unbounded initial data

2021 ◽  
Author(s):  
Haroldo Clark ◽  
Ronald Guardia
Keyword(s):  
Initial Data ◽  
Boundary Value Problems ◽  
Sobolev Spaces ◽  
Boundary Value ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Kirchhoff Type ◽  
Initial Boundary Value ◽  
Kirchhoff Type Problems

This paper deals with the existence, uniqueness and stability uniform of nonlocal solutions for initial-boundary value problems of the Kirchhoff type. The main purpose is to establish the exis- tence of at least one nonlocal solutions for degenerate Kirchhoff-type problems with initial data in the Sobolev spaces and without any restrictions on the size of their norms.

Sign in / Sign up

Export Citation Format

Share Document