The rice-straw mushroom (Volvariella volvacea) has a distinct flavor, pleasant taste, and rich protein content. It has low production costs and a cropping duration of approximately 45 days-making it an effective means for poverty alleviation for those farmers who grow it. Farmers in Vietnam, the Philippines, and Cambodia grow it. Rice straw is one of the most common substrates used for growing this mushroom. The mushroom can grow well in both outdoor and indoor conditions; however, outdoor cultivation has risks of exposure to rain, wind, and/or high temperatures, all which reduce yield. The yield of indoor mushroom production is higher and more stable, as such, indoor growing is preferred. In addition to cultivation, this chapter also covers straw mushroom characteristics, cultivation principles and techniques, and rice straw substrate preparation.

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We study the 2D magnetohydrodynamic (MHD) equations for a viscous incompressible resistive fluid, a system with the Navier-Stokes equations for the velocity field coupled with a convection-diffusion equation for the magnetic fields, in an arbitrary (bounded or unbounded) domain satisfying the Poincaré inequality with a large class of non-autonomous external forces. The existence of a weak solution to the problem is proved by using the Galerkin method. We then show the existence of a unique minimal pullback Dσ-attractor for the process associated to the problem. An upper bound on the fractal dimension of the pullback attractor is also given.

The global existence of weak solutions to a class of quasilinear parabolic equations with nonlinearities depending on first order terms and integrable data in a moving domain is investigated. The class includes the p-Laplace equation as a special case. Weak solutions are shown to be global by obtaining appropriate estimates on the gradient as well as a suitable version of Aubin-Lions lemma in moving domains. CONTENTS 1. Introduction 1 2. Uniform estimates 5 2.1. Uniform bounds of approximate solutions 6 2.2. Uniform bounds of the nonlinearity 13 3. Proof of Theorem 1.1 14 Appendix A. Existence of approximate solutions 22 Appendix B. An Aubin-Lions lemma in moving domains 26 References 27 2010 Mathematics Subject Classification. 35K59, 35K90, 35K92.

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