scholarly journals On weak solutions of semilinear hyperbolic-parabolic equations

1996 ◽  
Vol 19 (4) ◽  
pp. 751-758 ◽  
Author(s):  
Jorge Ferreira
Keyword(s):  
Parabolic Equation ◽  
Continuous Function ◽  
Weak Solutions ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Dirichlet Boundary ◽  
A Priori ◽  
A Priori Estimate ◽  
Dirichlet Boundary Conditions ◽  
Priori Estimate

In this paper we prove the existence and uniqueness of weak solutions of the mixed problem for the nonlinear hyperbolic-parabolic equation(K1(x,t)u′)′+K2(x,t)u′+A(t)u+F(u)=fwith null Dirichlet boundary conditions and zero initial data, whereF(s)is a continuous function such thatsF(s)≥0,∀s∈Rand{A(t);t≥0}is a family of operators ofL(H01(Ω);H−1(Ω)). For the existence we apply the Faedo-Galerkin method with an unusual a priori estimate and a result of W. A. Strauss. Uniqueness is proved only for some particular classes of functionsF.

scholarly journals A Mixed Problem with an Integral Two-Space-Variables Condition for Parabolic Equation with The Bessel Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Bouziani Abdelfatah ◽  
Oussaeif Taki-Eddine ◽  
Ben Aoua Leila
Keyword(s):  
Parabolic Equation ◽  
Mixed Problem ◽  
Existence And Uniqueness ◽  
Weighted Sobolev Space ◽  
A Priori ◽  
Energy Inequality ◽  
A Priori Estimate ◽  
Bessel Operator ◽  
Priori Estimate ◽  
Uniqueness Of The Solution

We study a mixed problem with an integral two-space-variables condition for parabolic equation with the Bessel operator. The existence and uniqueness of the solution in functional weighted Sobolev space are proved. The proof is based on a priori estimate “energy inequality” and the density of the range of the operator generated by the problem considered.

scholarly journals On a class of singular hyperbolic equation with a weighted integral condition

1999 ◽  
Vol 22 (3) ◽  
pp. 511-519 ◽  
Author(s):  
Said Mesloub ◽  
Abdelfatah Bouziani
Keyword(s):  
Hyperbolic Equation ◽  
Strong Solution ◽  
Existence And Uniqueness ◽  
Hyperbolic Equations ◽  
Nonlocal Condition ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Priori Estimate ◽  
Weighted Integral

In this paper, we study a mixed problem with a nonlocal condition for a class of second order singular hyperbolic equations. We prove the existence and uniqueness of a strong solution. The proof is based on a priori estimate and on the density of the range of the operator generated by the studied problem.

FINITE-DIFFERENCE METHODS FOR PROBLEM OF CONJUGATION OF HYPERBOLIC AND PARABOLIC EQUATIONS

2000 ◽  
Vol 10 (03) ◽  
pp. 361-377 ◽  
Author(s):  
ALEXANDER A. SAMARSKII ◽  
VICTOR I. KORZYUK ◽  
SERGEY V. LEMESHEVSKY ◽  
PETR P. MATUS
Keyword(s):  
Difference Scheme ◽  
Parabolic Equations ◽  
A Priori ◽  
Finite Difference Methods ◽  
A Priori Estimate ◽  
Stability And Convergence ◽  
Priori Estimate ◽  
Order Of Accuracy ◽  
Spatial Operator ◽  
The Given

A problem of conjugation of hyperbolic and parabolic equations in domain with moving boundaries is considered. Existence and uniqueness of a strong solution of the given problem are proved. A priori estimate for operator-difference scheme with non-self-adjoint spatial operator is obtain. Homogeneous difference scheme with constant weights for the conjugation problem is constructed. Moreover, consistency conditions are approximated with the second-order of accuracy with respect to spatial variables. Stability and convergence of the suggested scheme are investigated.

scholarly journals On three-point boundary value problem with a weighted integral condition for a class of singular parabolic equations

2002 ◽  
Vol 7 (10) ◽  
pp. 517-530 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
Boundary Value Problem ◽  
Parabolic Equations ◽  
Boundary Value ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Point Boundary ◽  
Priori Estimate ◽  
Weighted Integral ◽  
Singular Parabolic Equations

We deal with a three point boundary value problem for a class of singular parabolic equations with a weighted integral condition in place of one of standard boundary conditions. We will first establish an a priori estimate in weighted spaces. Then, we prove the existence, uniqueness, and continuous dependence of a strong solution.

scholarly journals The Solvability of First Type Boundary Value Problem for a Schrödinger Equation

2020 ◽  
Vol 5 (1) ◽  
pp. 211-220
Author(s):  
Nigar Yildirim Aksoy
Keyword(s):  
Schrödinger Equation ◽  
Boundary Value Problem ◽  
Existence And Uniqueness ◽  
Schrodinger Equation ◽  
Boundary Value ◽  
A Priori ◽  
A Priori Estimate ◽  
Uniqueness Theorems ◽  
Priori Estimate ◽  
Type Boundary

AbstractThe paper presents an first type boundary value problem for a Schrödinger equation. The aim of paper is to give the existence and uniqueness theorems of the boundary value problem using Galerkin’s method. Also, a priori estimate for its solution is given.

scholarly journals Mixed problem with a weighted integral condition for a parabolic equation with the Bessel operator

2002 ◽  
Vol 15 (3) ◽  
pp. 277-286 ◽  
Author(s):  
Said Mesloub ◽  
Abdelfatah Bouziani
Keyword(s):  
Parabolic Equation ◽  
Mixed Problem ◽  
Continuous Dependence ◽  
A Priori ◽  
A Priori Estimate ◽  
Integral Condition ◽  
Bessel Operator ◽  
Analysis Method ◽  
Priori Estimate ◽  
Weighted Integral

In this paper, we prove the existence, uniqueness and continuous dependence on the data of a solution of a mixed problem with a weighted integral condition for a parabolic equation with the Bessel operator. The proof uses a functional analysis method based on an a priori estimate and on the density of the range of the operator generated by the considered problem.

Parabolic equations with Cauchy–Dirichlet boundary conditions in a non-regular domain of ℝN+1

2014 ◽  
Vol 21 (2) ◽  
Author(s):  
Arezki Kheloufi
Keyword(s):  
Parabolic Equation ◽  
Boundary Conditions ◽  
Parabolic Equations ◽  
Dirichlet Boundary ◽  
Maximal Regularity ◽  
Dirichlet Boundary Conditions ◽  
Regular Domain

Abstract.New results on the existence, uniqueness and maximal regularity of a solution are given for a parabolic equation set in a non-regular domain

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