Invariant measures for stochastic parabolic-hyperbolic equations in the space of almost periodic functions: Lipschitz flux case

被引：0

作者：

Espitia, Claudia ^{[1
]}

Frid, Hermano ^{[2
]}

Marroquin, Daniel ^{[3
]}

机构：

[1] Inst Matemat Pura & Aplicada IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, RJ, Brazil

[2] FFCLRPUSP, Dept Computat & Math DCM, Ave Bandeirantes,3900, BR-14040901 Ribeirao Preto, SP, Brazil

[3] Univ Fed Rio de Janeiro, Inst Matemat, Cidade Univ, BR-21945970 Brazi, RJ, Brazil

来源：

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS | 2023年 / 20卷 / 03期

关键词：

Stochastic partial differential equations; scalar conservation laws; invariant measures; DIVERGENCE-MEASURE FIELDS; SCALAR CONSERVATION-LAWS; ENTROPY SOLUTIONS; WELL-POSEDNESS; CAUCHY-PROBLEM; TIME BEHAVIOR; DECAY; CONVERGENCE;

D O I：

10.1142/S0219891623500224

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the well-posedness and the long-time behavior of almost periodic solutions to stochastic degenerate parabolic-hyperbolic equations in any space dimension, under the assumption of Lipschitz continuity of the flux and viscosity functions and a non-degeneracy condition. We show the existence and uniqueness of an invariant measure in a separable subspace of the space of Besicovitch almost periodic functions.

引用

页码：745 / 792

页数：48

共 56 条

[1]

Ambrosio L., 2000, OX MATH M, pxviii

[2]

[Anonymous], 1957, Uspehi Mat. Nauk (N.S.)

[3]

[Anonymous], 2014, Encyclopedia of Mathematics and Its Applications

[4]

[Anonymous], 1983, Almost Periodic Functions and Differential Equations

[5]

[Anonymous], 1979, NONLINEAR ANAL MECH

[6]

[Anonymous], 1963, Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert space

[7] A degenerate parabolic-hyperbolic Cauchy problem with a stochastic force [J].

Bauzet, Caroline ;

Vallet, Guy ;

Wittbold, Petra .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2015, 12 (03) :501-533

[8] THE CAUCHY PROBLEM FOR CONSERVATION LAWS WITH A MULTIPLICATIVE STOCHASTIC PERTURBATION [J].

Bauzet, Caroline ;

Vallet, Guy ;

Wittbold, Petra .

JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2012, 9 (04) :661-709

[9] Renormalized entropy solutions for quasi-linear anisotropic degenerate parabolic equations [J].

Bendahmane, M ;

Karlsen, KH .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2004, 36 (02) :405-422

[10]

Besicovitch AS., 1932, Almost periodic functions

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