## Non-uniqueness of solution of tticomis problem for degenerating multidimensional mixed hyperbolic-parabolic equations

#### Citation

Orshubekov, N. (2009). Non-uniqueness of solution of tticomis problem for degenerating multidimensional mixed hyperbolic-parabolic equations. Maltepe Üniversitesi. s. 295.#### Abstract

Let D- final area of Euclidean space Em+1 of the points (x1, ..., xm, t) , limited in half-space t > 0 by cones K0 : |x| =
2
2+p
t
2+p
2 , K1 : |x| = 1 − 2
2+p
t
2+p
2 , 0 ≤ t ≤ (
2+p
4
)
2
2+p and at t < 0 - cylindrical surface Γ = {(x, t) : |x| = 1} and a plane
t = t0 < 0 , where |x| - vector-length and p = const > 0. Let’s designate through D+, D− the parts of domain D lying
respectively in half-paces t > 0 and t < 0. And parts of the cones K0, K1 limiting areas D+, well denote through S0 and
S1, accordingly. Let Γ = {(x, t) : t = 0, |x| = 1} . Consider following mixed modeling hyperbolic- parabolic equation in
area. Let D- final area of Euclidean space Em+1 of the points (x1, ..., xm, t) , limited in half-space t > 0 by cones K0 : |x| =
2
2+p
t
2+p
2 , K1 : |x| = 1 − 2
2+p
t
2+p
2 , 0 ≤ t ≤ (
2+p
4
)
2
2+p and at t < 0 - cylindrical surface Γ = {(x, t) : |x| = 1} and a plane
t = t0 < 0 , where |x| - vector-length and p = const > 0. Let’s designate through D+, D− the parts of domain D lying
respectively in half-paces t > 0 and t < 0. And parts of the cones K0, K1 limiting areas D+, well denote through S0 and
S1, accordingly. Let Γ = {(x, t) : t = 0, |x| = 1} . Consider following mixed modeling hyperbolic- parabolic equation in
area :
Let D- final area of Euclidean space Em+1 of the points (x1, ..., xm, t) , limited in half-space t > 0 by cones K0 : |x| =
2
2+p
t
2+p
2 , K1 : |x| = 1 − 2
2+p
t
2+p
2 , 0 ≤ t ≤ (
2+p
4
)
2
2+p and at t < 0 - cylindrical surface Γ = {(x, t) : |x| = 1} and a plane
t = t0 < 0 , where |x| - vector-length and p = const > 0. Let’s designate through D+, D− the parts of domain D lying
respectively in half-paces t > 0 and t < 0. And parts of the cones K0, K1 limiting areas D+, well denote through S0 and
S1, accordingly. Let Γ = {(x, t) : t = 0, |x| = 1} . Consider following mixed modeling hyperbolic- parabolic equation in
area :
Let D- final area of Euclidean space Em+1 of the points (x1, ..., xm, t) , limited in half-space t > 0 by cones K0 : |x| =
2
2+p
t
2+p
2 , K1 : |x| = 1 − 2
2+p
t
2+p
2 , 0 ≤ t ≤ (
2+p
4
)
2
2+p and at t < 0 - cylindrical surface Γ = {(x, t) : |x| = 1} and a plane
t = t0 < 0 , where |x| - vector-length and p = const > 0. Let’s designate through D+, D− the parts of domain D lying
respectively in half-paces t > 0 and t < 0. And parts of the cones K0, K1 limiting areas D+, well denote through S0 and
S1, accordingly. Let Γ = {(x, t) : t = 0, |x| = 1} . Consider following mixed modeling hyperbolic- parabolic equation in
area :
Let D- final area of Euclidean space Em+1 of the points (x1, ..., xm, t) , limited in half-space t > 0 by cones K0 : |x| =
2
2+p
t
2+p
2 , K1 : |x| = 1 − 2
2+p
t
2+p
2 , 0 ≤ t ≤ (
2+p
4
)
2
2+p and at t < 0 - cylindrical surface Γ = {(x, t) : |x| = 1} and a plane
t = t0 < 0 , where |x| - vector-length and p = const > 0. Let’s designate through D+, D− the parts of domain D lying
respectively in half-paces t > 0 and t < 0. And parts of the cones K0, K1 limiting areas D+, well denote through S0 and
S1, accordingly. Let Γ = {(x, t) : t = 0, |x| = 1} . Consider following mixed modeling hyperbolic- parabolic equation in
area.

#### Source

International Conference of Mathematical Sciences#### Collections

- Makale Koleksiyonu [586]

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