Galerkin methods for a semilinear parabolic problem with nonlocal boundary conditions

1996 ◽  
Vol 6 (1) ◽  
pp. 243-262 ◽  
Author(s):  
G. Fairweather ◽  
J. C. López-Marcos
Keyword(s):  
Boundary Conditions ◽  
Parabolic Problem ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Galerkin Methods ◽  
Semilinear Parabolic ◽  
Semilinear Parabolic Problem

scholarly journals Perturbation Analysis of a Semilinear Parabolic Problem with Nonlinear Boundary Conditions

1996 ◽  
Vol 26 (1) ◽  
pp. 195-212 ◽  
Author(s):  
A.A. Lacey ◽  
J.R. Ockendon ◽  
J. Sabina ◽  
D. Salazar
Keyword(s):  
Boundary Conditions ◽  
Perturbation Analysis ◽  
Parabolic Problem ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Conditions ◽  
Semilinear Parabolic ◽  
Semilinear Parabolic Problem

scholarly journals On a Semilinear Parabolic Problem with Four-Point Boundary Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 468
Author(s):  
Marián Slodička
Keyword(s):  
Boundary Conditions ◽  
Semigroup Theory ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Semilinear Parabolic Equation ◽  
Point Boundary ◽  
Constructive Algorithm ◽  
Transient Problem ◽  
Steady State Problem ◽  
Semilinear Parabolic

This paper studies a semilinear parabolic equation in 1D along with nonlocal boundary conditions. The value at each boundary point is associated with the value at an interior point of the domain, which is known as a four-point boundary condition. First, the solvability of a steady-state problem is addressed and a constructive algorithm for finding a solution is proposed. Combining this schema with the semi-discretization in time, a constructive algorithm for approximation of a solution to a transient problem is developed. The well-posedness of the problem is shown using the semigroup theory in C-spaces. Numerical experiments support the theoretical algorithms.

scholarly journals Quasilinearization for some nonlocal problems

1993 ◽  
Vol 6 (2) ◽  
pp. 117-122
Author(s):  
Yunfeng Yin
Keyword(s):  
Parabolic Equation ◽  
Boundary Conditions ◽  
Quadratic Convergence ◽  
Nonlocal Boundary ◽  
Nonlocal Boundary Conditions ◽  
Semilinear Parabolic Equation ◽  
Monotone Sequence ◽  
Nonlocal Problems ◽  
Semilinear Parabolic

The method of generalized quasilinearization [4] is applied to study semilinear parabolic equation ut−Lu=f(t,x,u) with nonlocal boundary conditions u(t,x)=∫Ωϕ(x,y)u(t,y)dy in this paper. The convexity of f in u is relaxed by requiring f(t,x,u)+Mu2 to be convex for some M>0. The quadratic convergence of monotone sequence is obtained.

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