scholarly journals On a global classical solution of a quasilinear hyperbolic equation

1989 ◽  
Vol 12 (1) ◽  
pp. 29-37 ◽  
Author(s):  
Y. Ebihara ◽  
D. C. Pereira
Keyword(s):  
Hyperbolic Equation ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Torsional Vibrations ◽  
Global Classical Solution ◽  
Quasilinear Hyperbolic Equation ◽  
Global Classical Solutions

In this paper we establish the existence and uniqueness of global classical solutions for the equation which arises in the study of the extensional vibrations of thin rod, or torsional vibrations of thin rod.

scholarly journals Global classical solutions to the Cauchy problem for a nonlinear wave equation

1998 ◽  
Vol 21 (3) ◽  
pp. 533-548 ◽  
Author(s):  
Haroldo R. Clark
Keyword(s):  
Cauchy Problem ◽  
Wave Equation ◽  
Classical Solution ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Global Classical Solution ◽  
Global Classical Solutions ◽  
The Cauchy Problem

In this paper we consider the Cauchy problem{u″+M(|A12u|2)Au=0   in   ]0,T[u(0)=u0,       u′(0)=u1,whereu′is the derivative in the sense of distributions and|A12u|is theH-norm ofA12u. We prove the existence and uniqueness of global classical solution.

scholarly journals A reaction infiltration problem: classical solutions

1997 ◽  
Vol 40 (2) ◽  
pp. 275-291 ◽  
Author(s):  
John Chadam ◽  
Xinfu Chen ◽  
Roberto Gianni ◽  
Riccardo Ricci
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Parabolic Equation ◽  
Elliptic Equation ◽  
Boundary Conditions ◽  
Classical Solution ◽  
Existence And Uniqueness ◽  
Classical Solutions ◽  
Bounded Domains ◽  
Global Classical Solution

In this paper, we consider a reaction infiltration problem consisting of a parabolic equation for the concentration, an elliptic equation for the pressure, and an ordinary differential equation for the porosity. Existence and uniqueness of a global classical solution is proved for bounded domains Ω⊂RN, under suitable boundary conditions.

THE GLOBAL CLASSICAL SOLUTION OF THE VLASOV–MAXWELL–FOKKER–PLANCK SYSTEM NEAR MAXWELLIAN

2011 ◽  
Vol 21 (05) ◽  
pp. 1007-1025 ◽  
Author(s):  
MYEONGJU CHAE
Keyword(s):  
Cauchy Problem ◽  
Electromagnetic Field ◽  
Classical Solution ◽  
Charged Particles ◽  
Classical Solutions ◽  
Global Classical Solution ◽  
Self Consistent ◽  
The Cauchy Problem ◽  
Fokker Planck

The Vlasov–Maxwell–Fokker–Planck system is used in modeling distribution of charged particles in plasma, where particles interact via collisions and through their self-consistent electromagnetic field. We prove the existence of global in time classical solutions to the Cauchy problem near Maxwellians.

scholarly journals Existence and uniqueness of global classical solutions to a two dimensional two species cancer invasion haptotaxis model

2018 ◽  
Vol 23 (10) ◽  
pp. 4397-4431
Author(s):  
Jan Giesselmann ◽  
◽  
Niklas Kolbe ◽  
Lukacova-MedvidovaMaria ◽  
Nikolaos Sfakianakis ◽  
...  
Keyword(s):  
Existence And Uniqueness ◽  
Cancer Invasion ◽  
Classical Solutions ◽  
Two Dimensional ◽  
Global Classical Solutions

scholarly journals Strongly damped semilinear equations

1995 ◽  
Vol 8 (4) ◽  
pp. 397-404 ◽  
Author(s):  
D. Bahuguna
Keyword(s):  
Existence And Uniqueness ◽  
Analytic Semigroups ◽  
Classical Solutions ◽  
Semilinear Equations ◽  
Forcing Term ◽  
Global Classical Solutions ◽  
Strongly Damped

A class of strongly damped semilinear equations is studied by using the theory of analytic semigroups. Conditions (on the nonlinear forcing term) are given under which the existence and uniqueness of local and global classical solutions are ensured.

scholarly journals On Solvability of an Inverse Boundary Value Problem for Pseudo Hyperbolic Equation of the Fourth Order

2015 ◽  
Vol 7 (2) ◽  
pp. 101
Author(s):  
Yashar T. Mehraliyev ◽  
Afaq F. Huseynova
Keyword(s):  
Hyperbolic Equation ◽  
Integral Equations ◽  
Fourth Order ◽  
Existence And Uniqueness ◽  
Fourier Method ◽  
Unknown Coefficient ◽  
Classical Solutions ◽  
Equivalent Problem ◽  
Inverse Boundary ◽  
Uniqueness Of The Solution

We analyze the solvability of the inverse boundary problem with an unknown  coefficient depended on time for the pseudo hyperbolic equation of fourth order with periodic and integral conditions.The initial problem is reduced to an equivalent problem. With the help of the Fourier method, the equivalent problem is reduced to a system of integral equations. The existence and uniqueness of the solution of the integral equations is proved. The obtained solution of the integral equations is also the only solution to the equivalent problem. Basing on the equivalence of the problems, the theorem of the existence and uniqueness of the classical solutions of the original problem is proved.

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