A Lax-Oleinik representation formula is established for nonautonomous Hamilton-Jacobi equations on general networks, yielding unique solutions via an action functional whose minimizers are Lipschitz continuous without excluding the Zeno phenomenon.
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The height function of TASEP with space-time discontinuous speed function converges to a deterministic limit given by a Lax-Oleinik variational formula that satisfies a discontinuous Hamilton-Jacobi equation.
The paper proves existence and uniqueness of optimal controls for indefinite LQ problems in jump-diffusion systems with random coefficients by constructing a generalized stochastic Riccati equation with jumps from an algebraic inverse flow, under uniform convexity.
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Lax-Oleinik formula for nonautonomous Hamilton-Jacobi equations on networks
A Lax-Oleinik representation formula is established for nonautonomous Hamilton-Jacobi equations on general networks, yielding unique solutions via an action functional whose minimizers are Lipschitz continuous without excluding the Zeno phenomenon.
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Hydrodynamic limits for TASEP with space-time discontinuities
The height function of TASEP with space-time discontinuous speed function converges to a deterministic limit given by a Lax-Oleinik variational formula that satisfies a discontinuous Hamilton-Jacobi equation.
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Indefinite Stochastic LQ Optimal Control for Jump-Diffusion Systems with Random Coefficients
The paper proves existence and uniqueness of optimal controls for indefinite LQ problems in jump-diffusion systems with random coefficients by constructing a generalized stochastic Riccati equation with jumps from an algebraic inverse flow, under uniform convexity.