Convergence in the Hölder Space of the Solutions to Problems for Parabolic Equations with Two Small Parameters in Boundary Condition

2018 ◽  
Vol 236 (4) ◽  
pp. 379-398
Author(s):  
G. I. Bizhanova
Keyword(s):  
Boundary Condition ◽  
Parabolic Equations ◽  
Holder Space ◽  
Hölder Space ◽  
Small Parameters

Solution of the nonregular problem for a parabolic equation with the time derivative in the boundary condition

2021 ◽  
pp. 1-35
Author(s):  
Galina Bizhanova
Keyword(s):  
Boundary Layer ◽  
Boundary Condition ◽  
Parabolic Equation ◽  
Small Parameter ◽  
Unique Solvability ◽  
Time Derivative ◽  
Holder Space ◽  
Hölder Space ◽  
Space Solution ◽  
Unperturbed Problem

There is studied the Hölder space solution u ε of the problem for parabolic equation with the time derivative ε ∂ t u ε | Σ in the boundary condition, where ε > 0 is a small parameter. The unique solvability of the perturbed problem and estimates of it’s solution are obtained. The convergence of u ε as ε → 0 to the solution of the unperturbed problem is proved. Boundary layer is not appeared.

scholarly journals Solution to a parabolic equation with integral type boundary condition

1993 ◽  
Vol 16 (4) ◽  
pp. 775-781
Author(s):  
Ignacio Barradas ◽  
Salvador Perez-Esteva
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Continuous Dependence ◽  
Linear Parabolic Equation ◽  
Type Condition ◽  
Integral Type ◽  
Holder Space ◽  
Hölder Space ◽  
Type Boundary ◽  
Type Boundary Condition

In this paper we study the existence, and continuous dependence of the solutionϑ=ϑ(x,t)on a Hölder spaceH2+γ,1+γ/2(Q¯τ)(Q¯τ=[0,1]×[0,τ],   0<γ<1)of a linear parabolic equation, prescribingϑ(x,0)=f(x),ϑx(1,τ)=g(τ)the integral type condition∫0bϑ(x,τ)dx=E(τ).

Complete blow-up for quasilinear degenerate parabolic equations

2000 ◽  
Vol 130 (4) ◽  
pp. 877-908 ◽  
Author(s):  
R. Suzuki
Keyword(s):  
Boundary Condition ◽  
Parabolic Equation ◽  
Parabolic Equations ◽  
Degenerate Parabolic Equation ◽  
Dirichlet Boundary ◽  
Blow Up ◽  
Sufficient Conditions ◽  
Degenerate Parabolic Equations ◽  
Degenerate Parabolic ◽  
Image Position

Non-negative post-blow-up solutions of the quasilinear degenerate parabolic equation in RN (or a bounded domain with Dirichlet boundary condition) are studied. Various sufficient conditions for complete blow-up of solutions are given.

The theory of symmetrical gravity waves of finite amplitude. I

1951 ◽  
Vol 208 (1095) ◽  
pp. 475-486 ◽  
Keyword(s):  
Boundary Condition ◽  
Gravity Waves ◽  
Finite Amplitude ◽  
Breaking Wave ◽  
Two Dimensional ◽  
Linear Boundary ◽  
Dimensional Problem ◽  
Infinite Depth ◽  
Linear Boundary Condition ◽  
Small Parameters

The two-dimensional problem of symmetric finite amplitude gravity waves in an incompressible fluid of infinite depth is treated by a method which first involves satisfying a non-linear boundary condition exactly. The higher approximations are obtained by the method of small parameters. The breaking-wave conditions are discussed and expressions are given for the free-surface equation, the kinetic and the potential energies of the fluid.

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