Pointwise Blow-Up Phenomena for a Dirichlet Problem
نویسندگان
چکیده
منابع مشابه
BLOW-UP AND NONGLOBAL SOLUTION FOR A FAMILY OF NONLINEAR HIGHER-ORDER EVOLUTION PROBLEM
In this paper we consider a kind of higher-order evolution equation as^{kt^{k} + ^{k&minus1}u/t^{k&minus1} +• • •+ut &minus{delta}u= f (u, {delta}u,x). For this equation, we investigate nonglobal solution, blow-up in finite time and instantaneous blow-up under some assumption on k, f and initial data. In this paper we employ the Test function method, the eneralized convexity method an...
متن کاملPointwise Bounds and Blow-up for Nonlinear Polyharmonic Inequalities
We obtain results for the following question where m ≥ 1 and n ≥ 2 are integers. Question. For which continuous functions f : [0, ∞) → [0, ∞) does there exist a continuous function ϕ : (0, 1) → (0, ∞) such that every C 2m nonnegative solution u(x) of 0 ≤ −∆ m u ≤ f (u) in B 2 (0)\{0} ⊂ R n satisfies u(x) = O(ϕ(|x|)) as x → 0 and what is the optimal such ϕ when one exists? Résumé Nous obtenons d...
متن کاملThe Blow-up Problem for Exponential Nonlinearities
We give a solution of the blow-up problem for equation u = e, with data close to constants, in any number of space dimensions: there exists a blow-up surface, near which the solution has logarithmic behavior; its smoothness is estimated in terms of the smoothness of the data. More precisely, we prove that for any solution of u = e with Cauchy data on t = 1 close to (ln 2; 2) in H(R) H (R), s is...
متن کاملExistence and blow-up of solution of Cauchy problem for the sixth order damped Boussinesq equation
In this paper, we consider the existence and uniqueness of the global solution for the sixth-order damped Boussinesq equation. Moreover, the finite-time blow-up of the solution for the equation is investigated by the concavity method.
متن کاملExistence Results for a Dirichlet Quasilinear Elliptic Problem
In this paper, existence results of positive classical solutions for a class of second-order differential equations with the nonlinearity dependent on the derivative are established. The approach is based on variational methods.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Partial Differential Equations
سال: 2011
ISSN: 0360-5302,1532-4133
DOI: 10.1080/03605302.2011.574304