On Second Order Nonlinear Equations with Rectilinear Characteristics

2000 ◽  
Vol 7 (2) ◽  
pp. 299-316 ◽  
Author(s):  
J. Gvazava
Keyword(s):  
Cauchy Problem ◽  
Closed Form ◽  
Mixed Type ◽  
Method Of Characteristics ◽  
Hyperbolic Equations ◽  
Class A ◽  
General Integral ◽  
Equations Of Mixed Type ◽  
Characteristic Roots ◽  
Special Equation

Abstract A class of quasilinear hyperbolic equations of mixed type whose characteristic roots are simultaneously characteristic invariants is found. For a special equation of this class, a general integral is constructed in terms of invariants in the closed form by using the method of characteristics. Based on the structure of families of characteristics, the initial Cauchy problem is investigated. The structure of the solution definition and regularity domains is defined using the properties of initial perturbations.

HOMOGENEOUS HYPERBOLIC EQUATIONS WITH COEFFICIENTS DEPENDING ON ONE SPACE VARIABLE

2007 ◽  
Vol 04 (03) ◽  
pp. 533-553 ◽  
Author(s):  
SERGIO SPAGNOLO ◽  
GIOVANNI TAGLIALATELA
Keyword(s):  
Cauchy Problem ◽  
Space Variable ◽  
Hyperbolic Equations ◽  
Diagonal Matrix ◽  
Well Posedness ◽  
Characteristic Roots ◽  
The Cauchy Problem

We investigate the Cauchy problem for homogeneous equations of order m in the (t,x)-plane, with coefficients depending only on x. Assuming that the characteristic roots satisfy the condition [Formula: see text] we succeed in constructing a smooth symmetrizer which behaves like a diagonal matrix: this allows us to prove the well-posedness in [Formula: see text].

scholarly journals Existence of Solutions of Nonlinear Stochastic Volterra Fredholm Integral Equations of Mixed Type

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
K. Balachandran ◽  
J.-H. Kim
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Mixed Type ◽  
Fixed Point Theorems ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Sufficient Conditions ◽  
Fredholm Integral Equations ◽  
Equations Of Mixed Type ◽  
Stochastic Integral Equations

We establish sufficient conditions for the existence and uniqueness of random solutions of nonlinear Volterra-Fredholm stochastic integral equations of mixed type by using admissibility theory and fixed point theorems. The results obtained in this paper generalize the results of several papers.

Sign in / Sign up

Export Citation Format

Share Document