Results 241 to 250 of about 104,532 (267)

Nonlinear hyperbolic volterra integrodifferential equations

Nonlinear Analysis: Theory, Methods & Applications, 1996
The well posedness of the abstract Cauchy problem \[ u'(t) = Au(t) + \int^t_{t_0} K \bigl( t,s,u(s) \bigr) ds + f(t), \quad u(t_0) = u_0 \] is studied, \(A\) denoting a linear Hille-Yosida operator in the Banach space \((X,II \cdot II)\). The paper consists of different Sections, and includes the proof of various theorems. The last Section refers to an
Nagel, Rainer, Sinestrari, Eugenio
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Oscillation Properties of Nonlinear Hyperbolic Equations

SIAM Journal on Mathematical Analysis, 1984
The authors derive a number of new oscillation criteria for hyperbolic equations. First of all, three theorems are proved, giving sufficient conditions for oscillation of solutions of the characteristic initial value problem \[ (2.2)\quad u_{xy}+c(x,y,u)=f(x,y),\quad u_ x(x,0)=g(x),\quad u_ y(0,y)=h(y), \] in an unbounded region contained in the ...
Kreith, Kurt, Kusano, Takaŝi, Yoshida, Norio   +2 more
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CENTERED DIFFERENCE SCHEMES FOR NONLINEAR HYPERBOLIC EQUATIONS

Journal of Hyperbolic Differential Equations, 2004
A hierarchy of centered (non-upwind) difference schemes is identified for solving hyperbolic equations. The bottom of the hierarchy is the classical Lax–Friedrichs scheme, which is the least accurate in computation, and the top of the hierarchy is the FORCE scheme, which is the optimal scheme in the family.
Chen, Gui-Qiang, Toro, Eleuterio F.
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Nonlinear Schrödinger Equation and the Hyperbolization Method

Computational Mathematics and Mathematical Physics, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Second Order Hyperbolic Equations with Small Nonlinearities

SIAM Journal on Applied Mathematics, 1978
A second order partial differential equation which describes the propagation of one-dimensional nonlinear waves in a bounded, inhomogeneous, dissipative medium is analyzed using the method of multiple scales. The conditions under which the oppositely traveling components of the nonlinear motion uncouple to first order are given.
Seymour, Brian R., Mortell, Michael P.
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On a Nonlinear Hyperbolic Volterra Equation

SIAM Journal on Mathematical Analysis, 1980
We study questions of existence, boundedness and asymptotic behavior of the solutions of the initial value problem \[(*)\qquad \begin{array}{*{20}c} {u_t (t,x) - \int_0^t {a (t - s)\sigma (u_x (s,x))_x = f(t,x),\quad 0 < t < \infty ,\quad x \in R.} } \\ {u(0,x) = u_0 (x),\quad x \in R.} \\ \end{array} \] Here $a:R^ + = [0,\infty ) \to R,\sigma :R \to R,
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On Nonlinear Hyperbolic Functional Differential Equations

Mathematische Nachrichten, 2000
The author proves existence of weak solutions of certain second-order evolution equations. The results are applied to higher-order nonlinear hyperbolic functional-differential equations.
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Symmetric hyperbolic equations in the nonlinear elasticity theory

Computational Mathematics and Mathematical Physics, 2008
Summary: Concerning the formulation of nonlinear elasticity equations in the form of symmetric hyperbolic systems, the article surveys basic results of long-time studies performed under the direction of the first author. The underlying principles developed therein are stated, and some inaccuracies and errors are corrected.
Godunov, S. K., Peshkov, I. M.
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Nonlinear Hyperbolic Equations

1996
Here we study nonlinear hyperbolic equations, with emphasis on quasi-linear systems arising from continuum mechanics, describing such physical phenomena as vibrating strings and membranes and the motion of a compressible fluid, such as air.
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Yosida approximation and nonlinear hyperbolic equation

Nonlinear Analysis: Theory, Methods & Applications, 1990
We are concerned with the initial value problem for nonlinear evolution equations of the form u″(t)+M(|A 1/2 u(t)| 2 )Au(t)+δu'(t)=f(t) on [0,∞), u(0)=u o , u'(O)=u 1 . Here A is a nonnegative selfadjoint operator in a real Hilbert space H,δ>0 is a constant and M is a C 1 -class function satisfying M(r)≥m o >0 for r≥0, with m o constant.
Ryo Ikehata, Noboru Okazawa
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