Generalized Solutions of a Class of Linear and Quasi-Linear Degenerated Hyperbolic Equations

Rossitza SEMERDJIEVA

Makale detayları

Generalized Solutions of a Class of Linear and Quasi-Linear Degenerated Hyperbolic Equations

Yazarlar:

Rossitza SEMERDJIEVA

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 1999 Vol.23 Issue 3, pp.375-388

Belge Tipi:

Makale

Yayın Tarihi:

2/1999

Belge Dili:

Türkçe

Document ID (Org No.):

2000749266

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Anahtar kelimeler:

Özet:

 

The equation L(u):=k(y)uxx-\partialy(\ell(y)uy)+r(x,y)u=f(x,y,u), where k(y)>0, \ell(y)>0 for y>0,k(0)=\ell(0)=0 and limy\rightarrow 0k(y)/\ell(y) exists, is strictly hyperbolic for y>0 and its order degenerates on the line y=0. We consider the boundary value problem Lu=f(x,y,u) in G, u\midAC=0, where G is a simply connected domain in R2 with piecewise smooth boundary \partial G=AB\cup AC\cup BC; AB=\{(x,0): 0\leq x\leq 1\}, AC : x=F(y) =\int0y(k(t)/\ell (t))1/2dt and BC: x=1-F(y) are characteristic curves. The existence and uniqueness of a generalized solution to this problem are proved in the linear case (where f=f(x,y)); the nonlinear case is treated by using the Schauder Fixed Point Theorem.

 

The equation L(u):=k(y)uxx-\partialy(\ell(y)uy)+r(x,y)u=f(x,y,u), where k(y)>0, \ell(y)>0 for y>0,k(0)=\ell(0)=0 and limy\rightarrow 0k(y)/\ell(y) exists, is strictly hyperbolic for y>0 and its order degenerates on the line y=0. We consider the boundary value problem Lu=f(x,y,u) in G, u\midAC=0, where G is a simply connected domain in R2 with piecewise smooth boundary \partial G=AB\cup AC\cup BC; AB=\{(x,0): 0\leq x\leq 1\}, AC : x=F(y) =\int0y(k(t)/\ell (t))1/2dt and BC: x=1-F(y) are characteristic curves. The existence and uniqueness of a generalized solution to this problem are proved in the linear case (where f=f(x,y)); the nonlinear case is treated by using the Schauder Fixed Point Theorem.

Makale detayları

Generalized Solutions of a Class of Linear and Quasi-Linear Degenerated Hyperbolic Equations

Yazarlar:

Rossitza SEMERDJIEVA

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 1999 Vol.23 Issue 3, pp.375-388

Belge Tipi:

Makale

Yayın Tarihi:

2/1999

Belge Dili:

Türkçe

Document ID (Org No.):

2000749266

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Turk. J. Math.

23

(1999)

375-388. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.23

iss.3.

Sayı

Makale detayları

Generalized Solutions of a Class of Linear and Quasi-Linear Degenerated Hyperbolic Equations

Yazarlar: Rossitza SEMERDJIEVA

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 1999 Vol.23 Issue 3, pp.375-388

Belge Tipi: Makale

Yayın Tarihi: 2/1999

Belge Dili: Türkçe

Document ID (Org No.): 2000749266

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Turk. J. Math.

23

(1999)

375-388. Full text: pdf Other articles published in the same issue: Turk. J. Math.

vol.23

iss.3.

Sayı

Yazarlar:

Rossitza SEMERDJIEVA

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 1999 Vol.23 Issue 3, pp.375-388

Belge Tipi:

Makale

Yayın Tarihi:

2/1999

Belge Dili:

Türkçe

Document ID (Org No.):

2000749266

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098