Porous media flow as the limit of a nonstrictly hyperbolic system of conservation laws

Journal Article · Mon Jul 01 04:00:00 EDT 1996 · Communications in Partial Differential Equations

DOI:https://doi.org/10.1080/03605309608821172· OSTI ID:255082

Rubino, B ^[1]

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1. Universita degi Studi di L` Aquila, Aquila (Italy)

We show here that the weak solutions of the quasilinear hyperbolic system ({epsilon}{upsilon} + ({var_epsilon}(n +1/2)({upsilon}{sup {epsilon}}){sup 2} + f({nu}{sup {epsilon}})){sub x} = -{upsilon}{sup {var_epsilon}} {nu}{sup {epsilon}}{sub +t} + ({nu}{sup {epsilon}}){sub x} =0 converge, as {epsilon} tends to zero, to the solutions of the reduced problem u + f({nu}{sub x}+0 {nu}{sub t}) + (u{nu}){sub x} =0 so that {nu} satisfies the nonlinear parabolic equation {nu}t-f({nu}){sub x}{nu}){sub x} =0. The limiting procedure is carried out by using the theory of compensated compactness. Finally we obtain the existence of Lyapounov functionals for the limit parabolic equation as weak limit to the convex entropies as {epsilon} tends to zero for the corresponding hyberbolic system.

• Sponsoring Organization: USDOE
• OSTI ID: 255082
• Journal Information: Communications in Partial Differential Equations, Journal Name: Communications in Partial Differential Equations Journal Issue: 1-2 Vol. 21; ISSN CPDIDZ; ISSN 0360-5302
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
99 GENERAL AND MISCELLANEOUS
CONSERVATION LAWS
CONVERGENCE
FLOW MODELS
FLUID FLOW
PARTIAL DIFFERENTIAL EQUATIONS
POROUS MATERIALS