Local solvability of an initial boundary value problem for a quasilinear hyperbolic-parabolic system

Yoshiyuki Kagei; Shuichi Kawashima

doi:10.1142/S0219891606000768

Local solvability of an initial boundary value problem for a quasilinear hyperbolic-parabolic system

Yoshiyuki Kagei, Shuichi Kawashima

Research output: Contribution to journal › Article › peer-review

34 Citations (Scopus)

Abstract

This paper investigates the solvability of initial boundary value problem for a quasilinear hyperbolic-parabolic system which consists of a transport equation and strongly parabolic system. The characteristics of the transport equation are assumed to be outward on the boundary of the domain. The unique local (in time) existence of solutions is shown in the class of continuous functions with values in H^s, where s is an integer satisfying s > [n/2]+1.

Original language	English
Pages (from-to)	195-232
Number of pages	38
Journal	Journal of Hyperbolic Differential Equations
Volume	3
Issue number	2
DOIs	https://doi.org/10.1142/S0219891606000768
Publication status	Published - Jun 2006

All Science Journal Classification (ASJC) codes

Analysis
Mathematics(all)

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10.1142/S0219891606000768

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abstract = "This paper investigates the solvability of initial boundary value problem for a quasilinear hyperbolic-parabolic system which consists of a transport equation and strongly parabolic system. The characteristics of the transport equation are assumed to be outward on the boundary of the domain. The unique local (in time) existence of solutions is shown in the class of continuous functions with values in Hs, where s is an integer satisfying s > [n/2]+1.",

author = "Yoshiyuki Kagei and Shuichi Kawashima",

year = "2006",

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AB - This paper investigates the solvability of initial boundary value problem for a quasilinear hyperbolic-parabolic system which consists of a transport equation and strongly parabolic system. The characteristics of the transport equation are assumed to be outward on the boundary of the domain. The unique local (in time) existence of solutions is shown in the class of continuous functions with values in Hs, where s is an integer satisfying s > [n/2]+1.

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Local solvability of an initial boundary value problem for a quasilinear hyperbolic-parabolic system

Abstract

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