The quasi-linear equation

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  • (BQ) Ebook Quasilinear hyperbolic systems, compressible flows, and waves: Part 1 includes the following content: Chapter 1 hyperbolic systems of conservation laws; chapter 2 scalar hyperbolic equations in one dimension; chapter 3 hyperbolic systems in one space dimension; chapter 4 evolution of weak waves in hyperbolic systems.

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  • (BQ) Ebook Quasilinear hyperbolic systems, compressible flows, and waves: Part 2 includes the following content: Chapter 5 asymptotic waves for quasilinear systems; chapter 6 self-similar solutions involving discontinuities; chapter 7 kinematics of a shock of arbitrary strength.

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  • In the paper "Liouville-type theorems for a quasilinear elliptic equation of the H´enon-type", We consider the H´enon-type quasilinear elliptic equation −Δmu = |x| aup where Δmu = div(|∇u| m−2∇u), m > 1, p>m − 1 and a ≥ 0. We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space RN . We prove the optimal Liouville-type theorem for dimension N

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  • In this paper, we study the first initial boundary value problem for a class of quasilinear degenerate parabolic equations involving weighted p-Laplacian operators. The existence and uniqueness of a weak solution with respect to initial values is ensured by an application of the Faedo - Galerkin approximation and compact method. Moreover, the longtime behavior of solutions to that problem is considered via the concept of global attractors in various bi-spaces.

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  • We propose a new monotone finite-difference scheme for the second-order local approximation on a nonuniform grid that approximates the Dirichlet initial boundary value problem (IBVP) for the quasi-linear convection-diffusion equation with unbounded nonlinearity, namely, for the Gamma equation obtained by transformation of the nonlinear Black-Scholes equation into a quasilinear parabolic equation. Using the difference maximum principle, a two-sided estimate and an a priori estimate in the c-norm are obtained for the solution of the difference schemes that approximate this equation.

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  • In this paper we prove the existence and uniqueness of weak solutions to a class of quasilinear degenerate parabolic equations involving weighted p-Laplacian operators by combining compactness and monotonicity methods.

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  • Recently we introduced the concept of Poincar´e chaos. In the present paper, by means of the Bebutov dynamical system, an unpredictable solution is considered as a generator of the chaos in a quasilinear system. The results can be easily extended to different types of differential equations.

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  • In this paper, we have given new definitions and obtained the unique solution of a fractional causal terminal value problem by combining the technique of generalized quasilinearization in the sense of upper and lower solutions.

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  • The existence problem is solved, and global pointwise estimates of solutions are obtained for quasilinear and Hessian equations of Lane-Emden type, including the following two model problems: −∆p u = uq + µ, Fk [−u] = uq + µ, u ≥ 0, on Rn , or on a bounded domain Ω ⊂ Rn . Here ∆p is the p-Laplacian defined by ∆p u = div ( u| u|p−2 ), and Fk [u] is the k-Hessian defined as the sum of k × k principal minors of the Hessian matrix D2 u (k = 1, 2, . . . ,...

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  • This article is concerned with local well-posedness of the Cauchy problem for second order quasilinear hyperbolic equations with rough initial data. The new results obtained here are sharp in low dimension. 1. Introduction 1.1. The results. We consider in this paper second order, nonlinear hyperbolic equations of the form (1.1) gij (u) ∂i ∂j u = q ij (u) ∂i u ∂j u on R × Rn , with Cauchy data prescribed at time 0, (1.2) u(0, x) = u0 (x) , ∂0 u(0, x) = u1 (x) .

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  • V an isometry, as in the theorem of Plancherel, is not just a weighted L2-norm on some measure space. This is due to the fact that the back transformation Z has a different expression on each branch, and this is caused by the ramification of the domain. It is not clear to us how one could find a family of generalized eigenfunctions leading to a spectral representation of A.

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  • ROTHE TIME-DISCRETIZATION METHOD APPLIED TO A QUASILINEAR WAVE EQUATION SUBJECT TO INTEGRAL CONDITIONS ABDELFATAH BOUZIANI AND NABIL MERAZGA Received 27 January 2004 and in revised form 12 February 2004 This paper presents a well-posedness result for an initial-boundary value problem with only integral conditions over the spatial domain for a one-dimensional quasilinear wave equation. The solution and some of its properties are obtained by means of a suitable application of the Rothe time-discretization method. 1.

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article On the Solvability of Superlinear and Nonhomogeneous Quasilinear Equations

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: L^{\infty} estimates of solutions for the quasilinear parabolic equation with nonlinear gradient term and L^1 data

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  • Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence and Nonexistence of Global Solutions of the Quasilinear Parabolic Equations with Inhomogeneous Terms

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  • Pharmacokinetics (t1/2) and the apparent volume of distribution Vapp (p. 28) by the equation: Vapp t1/2 = In 2 x –––– Cltot The smaller the volume of distribution or the larger the total clearance, the shorter is the half-life. In the case of drugs renally eliminated in unchanged form, the half-life of elimination can be calculated from the cumulative excretion in urine; the final total amount eliminated corresponds to the amount absorbed.

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