Related papers: Comment on: "New exact solutions for the Kawahara …
We show that any dissipative (measure-valued) solution of the compressible Euler system that complies with Dafermos' criterion of maximal dissipation is necessarily an admissible weak solution. In addition, we propose a simple, at most two…
Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and…
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
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The paper describes a number of simple but quite effective methods for constructing exact solutions of PDEs, that involve a relatively small amount of intermediate calculations. The methods employ two main ideas: (i) simple exact solutions…
The exact solutions of both the cubic Duffing equation and cubic-quintic Duffing equation are presented by using only leaf functions. In previous studies, exact solutions of the cubic Duffing equation have been proposed using functions that…
In this paper, we consider the Kawahara equation in a bounded interval and with a delay term in one of the boundary conditions. Using two different approaches, we prove that this system is exponentially stable under a condition on the…
Using Green$'$s function and operator techniques we give a closed expression for the response of a non-relativistic system interacting through confining, harmonic forces. The expression for the incoherent part permits rapid evaluation of…
A dispersive analysis of $\eta\to 3\pi$ decays has been performed in the past by many authors. The numerical analysis of the pertinent integral equations is hampered by two technical difficulties: i) The angular averages of the amplitudes…
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In many mathematical types of research, in order to solve the fuzzy fractional differential equations, we should transform these problems into crisp corresponding problems and by solving them the approximate solution can be obtained. The…
For an abelian, CM extension $H/F$ of a totally real number field $F$, we improve upon the reformulation of the Equivariant Tamagawa Number Conjecture for the Artin motive $h_{H/F}$ by Atsuta-Kataoka in \cite{Atsuta-Kataoka-ETNC} and extend…
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…
In this note we try to understand the blow-up of solutions to Nakao's problem by using nonlinear ordinary differential inequalities.
In a recent Physical Review Letter [1] Garcia and Nieto Vesperinas (GNV) dispute the claim of perfect lensing made in [2]. The thrust of the GVN paper is that the solutions proposed in [2] imply infinite energy density and are therefore…
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Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
In this paper we show some exact solutions for the Ito equation. These solutions are obtained by two methods: the tanh method and the projective Riccati equation method.