Weak Solution
Uniqueness of weak solution for nonlinear elliptic equations in divergence form
... In this paper, we demonstrate the uniqueness of weak solution of the Dirichlet problem for divergence structure elliptic equations of the form.. Here, we consider the same problem for we[r] ...
6
Blow-up and local weak solution for a modified two-component Camassa-Holm equations
... The purpose of this article is to study the well posedness, local weak solution, and blow-up for Cauchy problem (1.2) and (1.3). System (1.2) also conserves conservation laws. Our starting point is to ...
12
On a weak solution matching up with the double degenerate parabolic equation
... A weak solution matching up with the double degenerate parabolic equation is ...of weak solution is proved by a parabolically regularized ...of weak solutions is established independent ...
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Regularity criterion for a weak solution to the three-dimensional magneto-micropolar fluid equations
... cal solution can be extended to a global solution is a challenging open problem in the mathematical fluid mechanics. There are numerous important progresses on the fun- damental issue of the regularity for ...
12
Global existence of weak solution and regularity criteria for the 2D Bénard system with partial dissipation
... strong-weak solution (u, π , θ ) of the steady Bénard problem in a 2D quad- rangular cavity, heated/cooled on two opposite sides and thermally insulated on the other ...conduction-diffusion solution ...
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Hölder continuity of weak solution to a nonlinear problem with non-standard growth conditions
... We note that the starting point for any comparison and freezing argument in the setting of variable p(x)-growth problems is a quantitative higher integrability result. Hence, in order to obtain the interior ...
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The entropy weak solution to a generalized Degasperis Procesi equation
... From Lemmas . and ., we derive that the function u presented in Lemma . is a weak solution of problem () in the sense of Definition .. We have to verify that u satisfies the entropy inequalities in ...
8
Reverse Poincaré type inequalities for the weak solution of system of partial differential inequalities
... The first theorem for generalized domain and generalized weight function was given by Josip Peˇcari´c. Muhammad Shoaib Saleem and the M. Phil. student Mr. Abid Hussain developed the convolution technique and also gave the ...
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An Introductory View of the Weak Solution of the p Laplacian Equation
... We have shown that the weak solution are H¨ older continuous, we want to seek more regularity of the weak solution. In fact, even the gradients are locally H¨ older continuous. However, this ...
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General model of wood in typical coupled tasks, Part II. – Weak solution
... The weak solution of coupled stress-strain task with moisture/temperature dependency of material model was obtained in this ...simple solution was ...Suggested weak solution off ers ...
6
On weak solution of a hyperbolic differential inclusion with nonmonotone discontinuous nonlinear term
... In this paper, a hyperbolic differential inclusion with nonmonotone discontinuous and nonlinear term, which the generalized velocity acts as its variable, is studied and the existence and[r] ...
9
Compatibility conditions for the existence of weak solutions to a singular elliptic equation
... () solution u, then by choosing ϕ = u in the definition of weak solution of () (see the definition below) it follows that h(x)|u| –α dx = |∇ u| dx – k(x)|u| +β dx < ...
11
Existence of solutions for a class of porous medium type equations with lower order terms
... existence of a bounded weak solution to problem (P ) (see []), provided that F satisfies a sign condition. As F = and f ∈ W –,r (), the existence of solutions to problem (P ) has been discussed in []. ...
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PERFORMANCE ANALYSIS OF PARALLEL FLOW SINGLE AND DOUBLE EFFECT ABSORPTION CYCLES
... effect solution parallel flow cycle, since the weak solution leaving the absorber is distributed in two parts to flow in parallel, one going to the main generator and the other to the secondary ...
7
On a stochastic Burgers equation with Dirichlet boundary conditions
... nonnegative weak solution of ...a weak solution for this system and use the method of Le Gall [14] to obtain pathwise uniqueness of weak ...strong solution x ...
12
Undercompressive shocks for scalar conservation laws with nonconvex fluxes
... on the role of undercompressive shock waves in solving Riemann problems for equation (1.1). A Riemann problem is a prototypical initial value problem in which the initial data is piecewise constant with a single ...
26
Renormalized weak solutions to the three-dimensional steady compressible magnetohydrodynamic equations
... We are concerned with the Dirichlet problem of the three-dimensional steady viscous compressible magnetohydrodynamic (MHD) equations. It is proved that for any specific heat ratio γ > 1, the Dirichlet problem of the ...
20
Boundary regularity for elliptic systems with supquadratic growth
... for weak solutions of quasilinear elliptic systems with the supquadratic growth condition and obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary ...
13
HYDRODYNAMIC LIMIT OF THE BOLTZMANN-MONGE-AMPERE SYSTEM
... In [11] L. Hsiao and al. studied the convergence of the VPB system to the Incompressible Euler Equations. It is clear that the case Q(f ε , f ε ) = 0 corresponds to the the Vlasov- Monge-Amp` ere(VMA). This problem, was ...
7
Homogenization of a semilinear variational inequality in a thick multi level junction
... the weak solution to the homogenized problem ...this solution, the above argumentations are true for any subsequence of { ε } chosen at the beginning of the ...
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