Two mathematical problems related to the theory of combustion

Thesis/Dissertation · Fri Jan 01 04:00:00 EST 1982

OSTI ID:6010247

Bressan, A

The first part of this thesis is concerned with the implicit integrodifferential equation theta/sub t/ - ..delta.. theta = delta/sub e//sup theta/ + ..gamma.. - 1/..gamma.. 1/vol..cap omega.. ..integral../sub ..cap omega../ theta/sub t/ dy, describing the ignition period of a thermal explosion in a confined reactive gas. Assuming Dirichelet boundary conditions, the existence, uniqueness and continuous dependence of solutions are proven for general n-dimensional domains ..cap omega... For spherical domains further qualitative results are provided, concerning the global behavior of solutions and, in particular, the existence of a finite blow-up time. The second part of the thesis contains some existence results for solutions of an abstract evolution equation. Let A be the generator of a nonlinear semigroup T in a Banach space X, and let ..omega..l-A be m-accreative. Define nu/sub ..cap alpha../(x) = sup(t/sup 1-..cap alpha../e/sup -..omega..t/ absolute value AT(t)x; t > 0) + absolute value x. Given the Cauchy problem U = Au + f(u), u(0) = x/sub 0/, assuming that the restriction of f to nu/sub ..cap alpha../-bounded sets is continuous for some ..cap alpha.. < 1, a local and a global existence theorem are proven. These results provide a nonlinear analogue to the perturbation theory known for linear analytic semigroups; they were motivated by the study of the nonlinear, degenerate parabolic system of P.D.E.'s describing the dynamics of gas combustion.

• OSTI ID: 6010247
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
400800* -- Combustion
Pyrolysis
&amp; High-Temperature Chemistry
ANALYTICAL SOLUTION
CAUCHY PROBLEM
CHEMICAL REACTIONS
COMBUSTION
DIFFERENTIAL EQUATIONS
DIRICHLET PROBLEM
EQUATIONS
IGNITION
NONLINEAR PROBLEMS
OXIDATION
THERMOCHEMICAL PROCESSES